https://scholars.lib.ntu.edu.tw/handle/123456789/428469
標題: | A geometric approach to problems in birational geometry | 作者: | CHEN-YU CHI Yau, Shing-Tung |
關鍵字: | Classification; Pluricanonical systems; Pseudonorms; Torelli-type theorems; Varieties of general type | 公開日期: | 2008 | 卷: | 105 | 期: | 48 | 起(迄)頁: | 18696-18701 | 來源出版物: | Proceedings of the National Academy of Sciences of the United States of America | 摘要: | A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties. A fundamental question is the following: Given two mildly singular projective varieties with some of the first variety's pseudonormed spaces being isometric to the corresponding ones of the second variety's, can one construct a birational map between them that induces these isometries? In this work, a positive answer to this question is given for varieties of general type. This can be thought of as a theorem of Torelli type for birational equivalence. © 2008 by The National Academy of Sciences of the USA. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/428469 https://www.scopus.com/inward/record.uri?eid=2-s2.0-57749105463&doi=10.1073%2fpnas.0809030105&partnerID=40&md5=e7b8e1afaba43caf9b67887fcbb5bf13 |
ISSN: | 0027-8424 00278424 |
DOI: | 10.1073/pnas.0809030105 | SDG/關鍵字: | article; geometry; isometrics; mathematics; priority journal; spatial discrimination; Algorithms; Mathematics; Models, Statistical |
顯示於: | 數學系 |
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