What Determines an Algebraic Variety?: (AMS-216) (Annals of Mathematics Studies #216)
By: and and and
Sign Up Now!
Already a Member? Log In
You must be logged into UK education collection to access this title.
Learn about membership options,
or view our freely available titles.
- Synopsis
- 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.
- Copyright:
- 2023
Book Details
- Book Quality:
- Publisher Quality
- Book Size:
- 240 Pages
- ISBN-13:
- 9780691246833
- Related ISBNs:
- 9780691246802, 9780691246819
- Publisher:
- Princeton University Press
- Date of Addition:
- 07/24/23
- Copyrighted By:
- N/A
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.
Reviews
Other Books
- by János Kollár
- by Martin Olsson
- by Max Lieblich
- by Will Sawin
- in Nonfiction
- in Mathematics and Statistics