What Determines an Algebraic Variety? - (AMS-216) (Hardcover)

A pioneering new nonlinear approach to a fundamental question in algebraic geometry One of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics. Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.

General

Imprint:	Princeton University Press
Country of origin:	United States
Series:	Annals of Mathematics Studies
Release date:	July 2023
Authors:	János Kollár • Max Lieblich • Martin Olsson • Will Sawin
Dimensions:	235 x 156mm (L x W)
Format:	Hardcover
Pages:	240
ISBN-13:	978-0-691-24680-2
Categories:	Books Promotions
LSN:	0-691-24680-7
Barcode:	9780691246802

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