What Determines an Algebraic Variety? : (AMS-216) Hardback
by Janos Kollar, Max Lieblich, Martin Olsson, Will Sawin
Part of the Annals of Mathematics Studies series
Hardback
Description
A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne 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.
Information
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Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:240 pages, 4 b/w illus.
- Publisher:Princeton University Press
- Publication Date:25/07/2023
- Category:
- ISBN:9780691246802
Other Formats
- Paperback / softback from £53.35
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Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:240 pages, 4 b/w illus.
- Publisher:Princeton University Press
- Publication Date:25/07/2023
- Category:
- ISBN:9780691246802
