中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人：江 辰 教授（上海数学中心）
题 目：Birational boundedness of non-canonical calabi-yau 3-folds
时 间：2019.08.22（星期四），16:00-17:00
地 点：数学院南楼N224室
摘 要：Calabi–Yau varieties and Fano varieties are building blocks of varieties in the sense of birational geometry. They are expected to satisfying certain ？niteness. Recent progress on BAB Conjecture shows that certain Fano varieties form a bounded family. We are looking for the analogue for Calabi–Yau varieties. Here we consider very singular Calabi–Yau varieties, that is, Calabi–Yau varieties with non-canonical klt singularities, which are those Calabi–Yau varieties be-having most like Fano. I will show the birational boundedness result for noncanoncal klt Calabi–Yau 3-folds. It is related to Shokurov's conjecture on minimal log discrepancies of non-canonical singularities. A part of this talk is a joint work with W. Chen, G. Di Cerbo, J. Han, and R. Svaldi.
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报告人：刘文飞 教授（厦门大学）
题 目：Simple-connectedness of Fano log pairs with semi-log-canonical singularities
时 间：2019.08.22（星期四），14:45-15:45
地 点：数学院南楼N224室
摘 要：Fano manifolds are (complex) projective manifolds whose canonical class is anti-ample. It is now well-known that every Fano manifold is simply connected. In birational geometry, the notion of Fano manifolds is generalized to that of Fano log pairs, which allows singularities coming up naturally in the minimal model program. Correspondingly, the simple-connectedness of Fano pairs with log canonical singularities were proven by work of several authors.In this talk, I will report on a further generalization in this direction, saying that any union of slc strata of a Fano log pair with semi-log-canonical singularities is simply connected. In particular, Fano log pairs with semi-log canonical singularities are simply connected. This is joint work with Osamu Fujino.
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