by Cumrun Vafa, Eric Zaslow
Publisher: American Mathematical Society 2003
Number of pages: 950
The aim of the book is to provide a pedagogical introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the main part of the monograph is devoted to the proof of mirror symmetry from various viewpoints. More advanced topics are also discussed. In particular, topological strings at higher genera and the notion of holomorphic anomaly.
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by S.S. Abhyankar - 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.
by William Fulton - 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.
by Sudhir R. Ghorpade - 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.
by Robin Hartshorne - 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.