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Algebraic Geometry

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K-theory (7)

e-books in Algebraic Geometry category

Book cover: Introduction To Algebraical GeometryIntroduction To Algebraical Geometry
by - Oxford University Press ,
The author's aim has been to produce a book suitable to the beginner who wishes to acquire a sound knowledge of the more elementary parts of the subject, and also sufficient for the candidate for a mathematical scholarship.
(802 views)
Book cover: Multiplication of Vectors and Structure of 3D Euclidean SpaceMultiplication of Vectors and Structure of 3D Euclidean Space
by - viXra ,
This text is a motivational survey of geometric algebra in 3D. The intention here was to use simple examples and reader is referred to the independent problem solving. The active reading of text is recommended, with paper and pencil in hand.
(546 views)

Book cover: Lectures on the topological recursion for Higgs bundles and quantum curvesLectures on the topological recursion for Higgs bundles and quantum curves
by - arXiv ,
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the discovery of the relation between the topological recursion and the quantization of Hitchin spectral curves associated with Higgs bundles.
(1382 views)
Book cover: Current Developments in Algebraic GeometryCurrent Developments in Algebraic Geometry
by - Cambridge University Press ,
An introductory panorama of current progress in the field, addressed to both beginners and experts. This volume offers expository overviews of the state of the art in many areas of algebraic geometry. Prerequisites are kept to a minimum ...
(1824 views)
Book cover: Convex Bodies and Algebraic GeometryConvex Bodies and Algebraic Geometry
by - Springer ,
The theory of toric varieties describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications ...
(1253 views)
Book cover: Ample Subvarieties of Algebraic VarietiesAmple Subvarieties of Algebraic Varieties
by - Springer ,
These notes are an enlarged version of a three-month course of lectures. Their style is informal. I hope they will serve as an introduction to some current research topics, for students who have had a one year course in modern algebraic geometry.
(1500 views)
Book cover: Abel's Theorem and the Allied TheoryAbel's Theorem and the Allied Theory
by - Cambridge University Press ,
This classic book covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. Many of the ideas put forward are of continuing relevance today.
(2004 views)
Book cover: Geometric Complexity Theory: An Introduction for GeometersGeometric Complexity Theory: An Introduction for Geometers
by - arXiv ,
This is survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory. The article is written to be accessible to graduate students. Numerous open questions are presented.
(2865 views)
Book cover: Introduction to Algebraic GeometryIntroduction to Algebraic Geometry
by - Indian Institute of Technology Bombay ,
This text is a brief introduction to algebraic geometry. We will focus mainly on two basic results in algebraic geometry, known as Bezout's Theorem and Hilbert's Nullstellensatz, as generalizations of the Fundamental Theorem of Algebra.
(4070 views)
Book cover: From D-modules to Deformation Quantization ModulesFrom D-modules to Deformation Quantization Modules
by - UPMC ,
The aim of these lecture notes is first to introduce the reader to the theory of D-modules in the analytical setting and also to make a link with the theory of deformation quantization (DQ for short) in the complex setting.
(2382 views)
Book cover: Classical Algebraic Geometry: A Modern ViewClassical Algebraic Geometry: A Modern View
by - Cambridge University Press ,
The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.
(3199 views)
Book cover: Lectures on Birational GeometryLectures on Birational Geometry
by - arXiv ,
Topics covered: introduction into the subject, contractions and extremal rays, pairs and singularities, Kodaira dimension, minimal model program, cone and contraction, vanishing, base point freeness, flips and local finite generation, etc.
(2898 views)
Book cover: Lectures on Moduli of CurvesLectures on Moduli of Curves
by - Tata Institute of Fundamental Research ,
These lecture notes are based on some lectures given in 1980. The object of the lectures was to construct a projective moduli space for stable curves of genus greater than or equal two using Mumford's geometric invariant theory.
(3932 views)
Book cover: Lectures on Curves on Rational and Unirational SurfacesLectures on Curves on Rational and Unirational Surfaces
by - Tata Institute of Fundamental Research ,
From the table of contents: Introduction; Geometry of the affine line (Locally nilpotent derivations, Algebraic pencils of affine lines, Flat fibrations by the affine line); Curves on an affine rational surface; Unirational surfaces; etc.
(3946 views)
Book cover: Lectures on Torus Embeddings and ApplicationsLectures on Torus Embeddings and Applications
by - Tata Institute of Fundamental Research ,
Theory of torus embeddings has find many applications. The point of the theory lies in its ability of translating meaningful algebra-geometric phenomena into very simple statements about the combinatorics of cones in affine space over the reals.
(4099 views)
Book cover: Lectures on Expansion Techniques In Algebraic GeometryLectures on Expansion Techniques In Algebraic Geometry
by - Tata Institute Of Fundamental Research ,
From the table of contents: Meromorphic Curves; G-Adic Expansion and Approximate Roots; Characteristic Sequences of a Meromorphic Curve; The Fundamental Theorem and applications; Irreducibility, Newton's Polygon; The Jacobian Problem.
(4120 views)
Book cover: Lectures on Deformations of SingularitiesLectures on Deformations of Singularities
by - Tata Institute of Fundamental Research ,
These notes are based on a series of lectures given in 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. Contents: Formal Theory and Computations; Elkik's Theorems on Algebraization.
(3954 views)
Book cover: Lectures on An Introduction to Grothendieck's Theory of the Fundamental GroupLectures on An Introduction to Grothendieck's Theory of the Fundamental Group
by - Tata Institute of Fundamental Research ,
The purpose of this text is to give an introduction to Grothendieck's theory of the fundamental group in algebraic geometry with the study of the fundamental group of an algebraic curve over an algebraically closed field of arbitrary characteristic.
(3967 views)
Book cover: Lectures On Old And New Results On Algebraic CurvesLectures On Old And New Results On Algebraic Curves
by - Tata Institute Of Fundamental Research ,
The aim of this text is to give a proof, due to Hans Grauert, of an analogue of Mordell's conjecture. Contents: Introduction; Algebro-Geometric Background; Algebraic Curves; The Theorem of Grauert (Mordell's conjecture for function fields).
(4330 views)
Book cover: Stacks ProjectStacks Project
by ,
The stacks project aims to build up enough basic algebraic geometry as foundations for algebraic stacks. This implies a good deal of theory on commutative algebra, schemes, varieties, algebraic spaces, has to be developed en route.
(4652 views)
Book cover: Determinantal RingsDeterminantal Rings
by - Springer ,
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. The book gives a coherent treatment of the structure of determinantal rings. The approach is via the theory of algebras with straightening law.
(4895 views)
Book cover: Introduction to Algebraic Topology and Algebraic GeometryIntroduction to Algebraic Topology and Algebraic Geometry
by ,
Introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for algebraically integrable systems and the geometry of quantum field and string theory.
(5255 views)
Book cover: Lectures on Siegel's Modular FunctionsLectures on Siegel's Modular Functions
by - Tata Institute of Fundamental Research ,
Contents: Modular Group of Degree n; Symplectic group of degree n; Reduction Theory of Positive Definite Quadratic Forms; Fundamental Domain of the Modular Group of Degree n; Modular Forms of Degree n; Algebraic dependence of modular forms; etc.
(5528 views)
Book cover: Analysis on Homogeneous SpacesAnalysis on Homogeneous Spaces
by - Royal Institute of Technology Stockholm ,
The main goal of these notes is to give a proof of the basic facts of harmonic analysis on compact symmetric spaces and then to apply these to concrete problems involving things such as the Radon and related transforms on these spaces.
(3953 views)
Book cover: Strings and GeometryStrings and Geometry
by - American Mathematical Society ,
This volume highlights the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform.
(7230 views)
Book cover: Mirror SymmetryMirror Symmetry
by - American Mathematical Society ,
The book provides an introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the monograph is devoted to the proof of mirror symmetry from various viewpoints.
(6503 views)
Book cover: Lectures on Algebraic GroupsLectures on Algebraic Groups
by - University of Oregon ,
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.
(6073 views)
Book cover: Algorithms in Real Algebraic GeometryAlgorithms in Real Algebraic Geometry
by - Springer ,
The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
(6792 views)
Book cover: Introduction to Stokes StructuresIntroduction to Stokes Structures
by - arXiv ,
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one.
(4444 views)
Book cover: Linear Systems Theory and Introductory Algebraic GeometryLinear Systems Theory and Introductory Algebraic Geometry
by - Math Sci Press ,
Systems theory offers a unified mathematical framework to solve problems in a wide variety of fields. This mathematics is not of the traditional sort involved in engineering education, but involves virtually every field of modern mathematics.
(7530 views)
Book cover: Computations in Algebraic Geometry with Macaulay 2Computations in Algebraic Geometry with Macaulay 2
by - Springer ,
This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out.
(5742 views)
Book cover: Abelian VarietiesAbelian Varieties
by ,
Introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.
(7213 views)
Book cover: Modular Functions and Modular FormsModular Functions and Modular Forms
by ,
This is an introduction to the arithmetic theory of modular functions and modular forms, with an emphasis on the geometry. Prerequisites are the algebra and complex analysis usually covered in advanced undergraduate or first-year graduate courses.
(7243 views)
Book cover: Introduction to Projective VarietiesIntroduction to Projective Varieties
by - Universidad Complutense de Madrid ,
The scope of these notes is to present a soft and practical introduction to algebraic geometry, i.e. with very few algebraic requirements but arriving soon to deep results and concrete examples that can be obtained 'by hand'.
(4768 views)
Book cover: An Introduction to Semialgebraic GeometryAn Introduction to Semialgebraic Geometry
by - Universite de Rennes ,
Semialgebraic geometry is the study of sets of real solutions of systems of polynomial equations and inequalities. These notes present the first results of semialgebraic geometry and related algorithmic issues. Their content is by no means original.
(7347 views)
Book cover: An Introduction to Complex Algebraic GeometryAn Introduction to Complex Algebraic Geometry
by - Institut Fourier Grenoble ,
This is an advanced course in complex algebraic geometry presupposing only some familiarity with theory of algebraic curves or Riemann surfaces. The goal is to understand the Enriques classification of surfaces from the point of view of Mori-theory.
(5185 views)
Book cover: Lectures on Logarithmic Algebraic GeometryLectures on Logarithmic Algebraic Geometry
by - University of California, Berkeley ,
Logarithmic geometry deals with two problems in algebraic geometry: compactification and degeneration. Contents: The geometry of monoids; Log structures and charts; Morphisms of log schemes; Differentials and smoothness; De Rham and Betti cohomology.
(7355 views)
Book cover: Algebraic Geometry over the Complex NumbersAlgebraic Geometry over the Complex Numbers
by - Purdue University ,
Algebraic geometry is the geometric study of sets of solutions to polynomial equations over a field (or ring). In this book the author maintains a reasonable balance between rigor and intuition; so it retains the informal quality of lecture notes.
(7391 views)
Book cover: Introduction to Algebraic GeometryIntroduction to Algebraic Geometry
by ,
From the table of contents: Affine Varieties; Ideals and varieties. Hilbert's Basis Theorem. Regular functions and regular mappings. Projective and Abstract Varieties; Dimension Theory; Regular and singular points; Intersection theory.
(5944 views)
Book cover: Algebraic GeometryAlgebraic Geometry
by - University of Kaiserslautern ,
From the contents: Introduction; Affine varieties; Functions, morphisms, and varieties; Projective varieties; Dimension; Schemes; First applications of scheme theory; More about sheaves; Cohomology of sheaves; Intersection theory; Chern classes.
(7437 views)
Book cover: Current Topics in Complex Algebraic GeometryCurrent Topics in Complex Algebraic Geometry
by - Cambridge University Press ,
The 1992/93 year at the Mathematical Sciences Research Institute was devoted to Complex Algebraic Geometry. This volume collects articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change.
(8846 views)
Book cover: Algebraic Groups and Discontinuous SubgroupsAlgebraic Groups and Discontinuous Subgroups
by - American Mathematical Society ,
The book covers linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups, automorphic functions and spectral decomposition of L2-spaces, vector valued cohomology and deformation of discrete subgroups, etc.
(8935 views)
Book cover: Mixed MotivesMixed Motives
by - American Mathematical Society ,
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry.
(8837 views)
Book cover: Quasi-Projective Moduli for Polarized ManifoldsQuasi-Projective Moduli for Polarized Manifolds
by - Springer ,
This book discusses two subjects of quite different nature: Construction methods for quotients of quasi-projective schemes by group actions or by equivalence relations and properties of direct images of certain sheaves under smooth morphisms.
(5858 views)
Book cover: Algebraic GeometryAlgebraic Geometry
by ,
These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, not just subvarieties of affine and projective space. This approach leads naturally to scheme theory.
(9182 views)
Book cover: Algebraic geometry and projective differential geometryAlgebraic geometry and projective differential geometry
by - arXiv ,
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, and more.
(9529 views)
Book cover: Complex Analytic and Differential GeometryComplex Analytic and Differential Geometry
by - Universite de Grenoble ,
Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.
(10771 views)
Book cover: Algebraic Curves: an Introduction to Algebraic GeometryAlgebraic Curves: an Introduction to Algebraic Geometry
by - Benjamin ,
These notes develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. It assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials.
(9568 views)
Book cover: Homogeneous Spaces and Equivariant EmbeddingsHomogeneous Spaces and Equivariant Embeddings
by - arXiv ,
A monograph on homogeneous spaces of algebraic groups and their equivariant embeddings. Some results are supplied with proofs, the other are cited with references to the original papers. The style is intermediate between survey and detailed monograph.
(6027 views)
Book cover: Geometry UnboundGeometry Unbound
by ,
This is not a typical math textbook, it does not present full developments of key theorems, but it leaves strategic gaps in the text for the reader to fill in. The original text underlying this book was a set of notes for the Math Olympiad Program.
(9062 views)