What Determines an Algebraic Variety? / Annals of Mathematics Studies Bd.216 (PDF)
One of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates,...
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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.
- Autoren: János Kollár , Max Lieblich , Martin Olsson , Will Sawin
- 2023, 240 Seiten, Englisch
- Verlag: The American University in Cairo Press
- ISBN-10: 0691246831
- ISBN-13: 9780691246833
- Erscheinungsdatum: 25.07.2023
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Grösse: 1.86 MB
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