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: |
Paperback
|
| Pages: |
240 |
| ISBN-13: |
978-0-691-24681-9 |
| Categories: |
Books
|
| LSN: |
0-691-24681-5 |
| Barcode: |
9780691246819 |
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