by J.S. Milne
Number of pages: 241
These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory.
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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.
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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.
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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.
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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.