中科院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

学术报告

多复变与复几何研讨班

SCV&CG Seminar

报告人：Shin-ichi Matsumura (Tohoku University)

题  目：The nonvanishing problem for varieties with nef anticanonical bundle

时  间：2023.09.27（星期三）14:30-16:30

地  点：南楼N913

摘  要：In this talk, I discuss the nonvanishing problem in the framework of the ''generalized'' Minimal Model Program. I first explain a structure theorem for maximally rationally connected fibrations of projective klt pairs with nef anticanonical divisor, which generalizes Cao-Horing's result for smooth projective varieties. I also show that this structure theorem reduces the nonvanishing problem for nef anticanonical divisors to the rationally connected varieties, and that the numerical class of the nef anticanonical bundle of projective 3-folds is represented by an effective divisor. The first part of this talk is joint work with Juanyong Wang (Chinese Academy of Sciences) and the latter part is joint work with Thomas Peternell (Bayreuth), Vladimir Lazic, Nikolaos Tsakanikas, Zhixin Xie (Saarbrucken).