What Determines An Algebraic Variety?: (Ams-216) (Annals Of Mathematics Studies, 216)

In this monograph, the authors approach a rarely considered question in the field of algebraic geometry: to what extent is an algebraic variety X determined by the underlying Zariski topological space ]X]? Before this work, it was believed that the Zariski topology could give only coarse information about X. Using three reconstruction theorems, the authors prove -- astoundingly -- that the variety X is entirely determined by the Zariski topology when the dimension is at least two. It offers both new techniques, as this question had not been previously studied in depth, and future paths for application and inquiry--

• | Author: János Kollár, Max Lieblich, Martin Olsson, Will Sawin
• | Publisher: Princeton University Press
• | Publication Date: Jul 25, 2023
• | Number of Pages: 240 pages
• | Language: English
• | Binding: Paperback
• | ISBN-10: 0691246815
• | ISBN-13: 9780691246819