bokomslag What Determines an Algebraic Variety?
Vetenskap & teknik

What Determines an Algebraic Variety?

Jnos Kollr Max Lieblich Martin Olsson Will Sawin

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  • 240 sidor
  • 2023
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.
  • Författare: Jnos Kollr, Max Lieblich, Martin Olsson, Will Sawin
  • Illustratör: 4 b, w illus
  • Format: Pocket/Paperback
  • ISBN: 9780691246819
  • Språk: Engelska
  • Antal sidor: 240
  • Utgivningsdatum: 2023-07-25
  • Förlag: Princeton University Press