Computations in Algebraic Geometry with Macaulay 2
by D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels
Publisher: Springer 2001
Number of pages: 343
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. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications.
Home page url
Download or read it online for free here:
by Andreas Gathmann - 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.
by D. Gieseker - 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.
by J.M. Landsberg - 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.
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.