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タイトル: | The Calabi Conjecture and K-stability |
著者: | Odaka, Yuji |
著者名の別形: | 尾高, 悠志 |
発行日: | Jun-2011 |
出版者: | Oxford University Press |
誌名: | International Mathematics Research Notices |
巻: | 2012 |
号: | 10 |
開始ページ: | 2272 |
終了ページ: | 2288 |
抄録: | We algebraically prove K-stability of polarized Calabi–Yau varieties and canonically polarized varieties with mild singularities. In particular, the “stable varieties” introduced by Kollár–Shepherd-Barron [“Threefolds and deformation of surface singularities.” Inventiones Mathematicae 91 (1988): 299–338] and Alexeev [“Moduli spaces Mg, n(W) for surfaces.” Proceeding of “Higher-dimensional complex varieties (Trento, 1994)”, de Gruyter, Berlin, 1996, 1–22], which form compact moduli space, are proven to be K-stable although it is well known that they are not necessarily asymptotically (semi) stable. As a consequence, we have orbifold counterexamples to the folklore conjecture “K-stability implies asymptotic stability”. They have Kähler–Einstein (orbifold) metrics, so the result of Donaldson [“Scalar curvature and projective embeddings. I.” Journal of Differential Geometry 59, no. 3 (2001): 479–522] does not hold for orbifolds. |
著作権等: | © The Author(s) 2011. Published by Oxford University Press. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/172079 |
DOI(出版社版): | 10.1093/imrn/rnr107 |
出現コレクション: | 学術雑誌掲載論文等 |
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