by Johan de Jong, et al.
Number of pages: 3428
An open source textbook on algebraic stacks and the algebraic geometry that is needed to define them. The Stacks Project builds the foundations starting with commutative algebra and proceeding via the theory of schemes and algebraic spaces to a comprehensive foundation for the theory of algebraic stacks.
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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 Alexander Kleshchev - 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.
by Gwyn Bellamy, et al. - Cambridge University Press
This book provides an introduction to some of the most significant topics in this area, including noncommutative projective algebraic geometry, deformation theory, symplectic reflection algebras, and noncommutative resolutions of singularities.
by Tadao Oda - 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.