by Kiran S. Kedlaya
Number of pages: 142
The original text underlying this book was a set of notes for the Math Olympiad Program, the annual summer program to prepare U.S. high school students for the International Mathematical Olympiad. The original notes were intended to bridge the gap between the knowledge of Euclidean geometry of American IMO prospects and that of their counterparts from other countries. They included a large number of challenging problems culled from Olympiad-level competitions from around the world. In revising the old text, author attempted to usher the reader from Euclidean geometry to the gates of "geometry" as the term is defined by modern mathematicians, using the solving of routine and nonroutine problems as the vehicle for discovery.
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by Marc Levine - American Mathematical Society
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry.
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.
by Michael Artin - Tata Institute of Fundamental Research
These notes are based on a series of lectures given in 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. Contents: Formal Theory and Computations; Elkik's Theorems on Algebraization.
by Caucher Birkar - arXiv
Topics covered: introduction into the subject, contractions and extremal rays, pairs and singularities, Kodaira dimension, minimal model program, cone and contraction, vanishing, base point freeness, flips and local finite generation, etc.