Current Topics in Complex Algebraic Geometry
by Herbert Clemens, János Kollár
Publisher: Cambridge University Press 1996
Number of pages: 172
The 1992/93 academic year at the Mathematical Sciences Research Institute was devoted to Complex Algebraic Geometry. This volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. To put it succinctly, algebraic geometry has opened up to ideas and connections from other fields that have traditionally been far away.
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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 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 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 J. S. Milne
Introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.