On flops and canonical metrics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866917841401282560 |
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| author | Cheltsov, Ivan A. Rubinstein, Yanir A. |
| author_facet | Cheltsov, Ivan A. Rubinstein, Yanir A. |
| contents | This article is concerned with an observation for proving non-existence of canonical Kahler metrics. The idea is to use a rather explicit type of degeneration that applies in many situations. Namely, in a variation on a theme introduced by Ross-Thomas, we consider flops of the deformation to the normal cone. This yields a rather widely applicable notion of stability that is still completely explicit and readily computable, but with wider scope. We describe some applications, among them, a proof of one direction of the Calabi conjecture for asymptotically logarithmic del Pezzo surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1508_04634 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | On flops and canonical metrics Cheltsov, Ivan A. Rubinstein, Yanir A. Algebraic Geometry Differential Geometry 14E05, 32Q25 (Primary), 14J45, 53C25, 53C55 (Secondary) This article is concerned with an observation for proving non-existence of canonical Kahler metrics. The idea is to use a rather explicit type of degeneration that applies in many situations. Namely, in a variation on a theme introduced by Ross-Thomas, we consider flops of the deformation to the normal cone. This yields a rather widely applicable notion of stability that is still completely explicit and readily computable, but with wider scope. We describe some applications, among them, a proof of one direction of the Calabi conjecture for asymptotically logarithmic del Pezzo surfaces. |
| title | On flops and canonical metrics |
| topic | Algebraic Geometry Differential Geometry 14E05, 32Q25 (Primary), 14J45, 53C25, 53C55 (Secondary) |
| url | https://arxiv.org/abs/1508.04634 |