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, János Kollár, Max Lieblich, Martin Olsson, Olsson Martin, Will Sawin
• Publisher: Princeton University Press
• Languages: English
• Product format: Paperback / Softback
• Released: 25.07.2023
• EAN: 9780691246819
• ISBN: 978-0-691-24681-9
• No. of pages: 240
• Series: Annals of Mathematics Studies
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; MATHEMATICS / Geometry / Algebraic, Algebraic Geometry