What Determines an Algebraic Variety? (Paperback)
Language: English
Published by Princeton University Press, New Jersey, 2023
- Softcover
- New
Seller: AussieBookSeller, Truganina, VIC, AustraliaAussieBookSeller
AbeBooks seller since June 22, 2007
Condition: New
£ 132.32
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Seller Inventory # 9780691246819
- Title
- What Determines an Algebraic Variety? (Paperback)
- Author
- Max Lieblich
- Publisher
- Princeton University Press, New Jersey
- Publication year
- 2023
- Condition
- new
- Binding
- Paperback
- Language
- English
- ISBN 10
- 0691246815
- ISBN 13
- 9780691246819
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.
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AussieBookSeller
Truganina, VIC, Australia
AbeBooks seller since June 22, 2007
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