Algebraic Curves: an Introduction to Algebraic Geometry
by William Fulton
Publisher: Benjamin 1969
Number of pages: 129
The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.
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by P. Samuel - 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).
by Olivia Dumitrescu, Motohico Mulase - 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.
by Tadao Oda - 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 ...
by Masayoshi Miyanishi - 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.