What Determines an Algebraic Variety? Ams-216

"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"--

About the author

János Kollár, Max Lieblich, Martin Olsson, and Will Sawin

Product details

• Authors: Janos Lieblich Kollar, Olsson Martin, Will Sawin, Martin Olsson, Max Lieblich, János Kollár
• Publisher: Princeton University Press
• Content: Book
• Product form: Paperback / Softback
• Publication date: 25.07.2023
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry
• EAN: 9780691246819
• ISBN: 978-0-691-24681-9
• Pages: 240
• Series: Annals of Mathematics Studies
• Subjects: Dimension, positive, Space, Weil, Line, Map, Zero, Bundle, variety, Integral, Function, MATHEMATICS / Geometry / Algebraic, Cartier, Linear, Torsion, Structure, rational, Elements, Pencil, Field, extension, Theorem, Component, Results, Points, Algebraic Geometry, finite, closure, Infinite, equivalence, unique, DiM, fiber, Effective, Topological, Morphism, isomorphism, sheaf, Locus, Complete, Intersection, Curve, Divisor, Scheme, degree, section, Algebraic, Subset, smooth, Dense, Dimensional, Equivalent, Denote, Assume, Finitely, Projective, Quasi, Suffices, Nonempty, Definable, Ample divisor, Divisorial, Zariski, Disjoint, Ample, Abelian, Algebraically, Hilbertian, Algebraically closed, Separable, Geometrically, Irreducible