| LDR | | 00000nam u2200205 4500 |
| 001 | | 000000433431 |
| 005 | | 20200225141412 |
| 008 | | 200131s2019 ||||||||||||||||| ||eng d |
| 020 | |
▼a 9781085772563 |
| 035 | |
▼a (MiAaPQ)AAI13884918 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Zhuang, Ziquan. |
| 245 | 10 |
▼a Birational Superrigidity and K-stability. |
| 260 | |
▼a [S.l.]:
▼b Princeton University.,
▼c 2019. |
| 260 | 1 |
▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
| 300 | |
▼a 98 p. |
| 500 | |
▼a Source: Dissertations Abstracts International, Volume: 81-04, Section: B. |
| 500 | |
▼a Advisor: Kollar, Janos. |
| 502 | 1 |
▼a Thesis (Ph.D.)--Princeton University, 2019. |
| 506 | |
▼a This item must not be sold to any third party vendors. |
| 520 | |
▼a We consider two different notions on Fano varieties: birational superrigidity, coming from the study of rationality, and K-stability, which is related to the existence of K"ahler-Einstein metrics. In the first part, we show that birationally superrigid Fano varieties are also K-stable as long as their alpha invariants are at least 쩍, partially confirming a conjecture of Odaka-Okada and Kim-Okada-Won. In the second part, we prove the folklore prediction that smooth Fano complete intersections of Fano index one are birationally superrigid and K-stable when the dimension is large. In the third part, we introduce an inductive argument to study the birational superrigidity and K-stability of singular complete intersections and in particular prove an optimal result on the birational superrigidity and K-stability of hypersurfaces of Fano index one with isolated ordinary singularities in large dimensions. Finally we provide an explicit example to show that in general birational superrigidity is not a locally closed property in families of Fano varieties, giving a negative answer to a question of Corti. |
| 590 | |
▼a School code: 0181. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a Princeton University.
▼b Mathematics. |
| 773 | 0 |
▼t Dissertations Abstracts International
▼g 81-04B. |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0181 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2019 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15491402
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
| 980 | |
▼a 202002
▼f 2020 |
| 990 | |
▼a ***1816162 |
| 991 | |
▼a E-BOOK |