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Conference Paper: Cluster category and birational geometry
| Title | Cluster category and birational geometry |
|---|---|
| Authors | |
| Issue Date | 2018 |
| Citation | Algebra seminar, University of Science and Technology of China (USTC), Hefei, China, 25 July 2018 How to Cite? |
| Abstract | A fundamental problem in birational geometry, in particular in minimal model program, is to classify contractible rational curves. In this talk, we will build a relation between it and the theory of cluster category. To be more specific, we associate to each 3-dimensional flopping contraction a cluster category in the sense of Aimot. Based on our previous work on noncommutative Mather-Yau theorem, we show that the cluster category is essentially determined by its cluster tilting algebra. On the other hand, we formulate certain necessary condition on the associated cluster category for a rigid rational curve to be contractible, which is conjectually to be also sufficient. The talk is based on a joint work with Guisong zhou 1803.06128. |
| Persistent Identifier | http://hdl.handle.net/10722/270467 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Hua, Z | - |
| dc.date.accessioned | 2019-05-29T01:53:03Z | - |
| dc.date.available | 2019-05-29T01:53:03Z | - |
| dc.date.issued | 2018 | - |
| dc.identifier.citation | Algebra seminar, University of Science and Technology of China (USTC), Hefei, China, 25 July 2018 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/270467 | - |
| dc.description.abstract | A fundamental problem in birational geometry, in particular in minimal model program, is to classify contractible rational curves. In this talk, we will build a relation between it and the theory of cluster category. To be more specific, we associate to each 3-dimensional flopping contraction a cluster category in the sense of Aimot. Based on our previous work on noncommutative Mather-Yau theorem, we show that the cluster category is essentially determined by its cluster tilting algebra. On the other hand, we formulate certain necessary condition on the associated cluster category for a rigid rational curve to be contractible, which is conjectually to be also sufficient. The talk is based on a joint work with Guisong zhou 1803.06128. | - |
| dc.language | eng | - |
| dc.relation.ispartof | University of Science and Technology of China (USTC), Algebra Seminar | - |
| dc.title | Cluster category and birational geometry | - |
| dc.type | Conference_Paper | - |
| dc.identifier.email | Hua, Z: huazheng@hku.hk | - |
| dc.identifier.authority | Hua, Z=rp01790 | - |
| dc.identifier.hkuros | 289665 | - |