北京代数几何日
BEIJING ALGEBRAIC GEOMETRY DAY
2025年2月22日 @清华大学，双清综合楼C548
会议组织单位：首都师范大学、中国科学院、北京大学、清华大学。
报名截止日期：2025年2月15日
报名链接：http://wenjuan.tsinghua.edu.cn/s/ZZZfuu/
上午
9：30-10：30 谢俊逸 （北京大学）
Numerical spectrums control cohomological spectrums
10：30-10：45 讨论/休息
10：45-11：45 郝峰（山东大学）
Good minimal models with nowhere vanishing holomorphic 1-forms
11：45-13：30 午餐
下午
13：30-14：30 欧文浩（中国科学院）
A characterization of uniruled Kaehler manifolds
14：30-14：45 讨论/休息
14：45-15：45 戚鲁（华东师范大学）
Stable degeneration of Fano fibrations and birational geometry
15：45-16：00 讨论/休息
16：00-17：00 吴小行（武汉科技大学）
On adjoint divisors for foliated surfaces
题目与摘要
谢俊逸 （北京大学）
题目：Numerical spectrums control cohomological spectrums
摘要：Let f be an endomorphism of projective variety. We show that the spectral radius of the pull-back of f on the numerical groups of codimension i and the l-adic cohomology group of degree 2i are the same. As a consequence, if f is q-polarized for some q>1, we show that every eigenvalue of the pull-back of f on the j-th cohomology group is qj/2. This generalizes Delignes’s theorem for Weil’s Riemann Hypothesis to arbitrary polarized endomorphisms and proves a conjecture of Tate.
郝峰（山东大学）
题目：Good minimal models with nowhere vanishing holomorphic 1-forms
摘要：Holomorphic 1-forms play a key role in the study of irregular algebraic varieties. A celebrated result of Popa and Schnell says that any holomorphic 1-form on a smooth projective variety of general type has zeros. This indicates that the existence of holomorphic 1-form without zero has a strong restriction on varieties. In this talk, We explain that a smooth good minimal model has a holomorphic 1-form without zero if and only if it admits an analytic fiber bundle structure over a positive dimensional abelian variety. This is a joint work with Zichang Wang and Lei Zhang.
欧文浩（中国科学院）
题目：A characterization of uniruled Kaehler manifolds
摘要：We prove a criterion for foliations on compact Kaehler manifolds which are induced by meromorphic maps. As an application, we prove that a compact Kaehler manifold is uniruled if and only if its canonical line bundle is not pseudoeffective.
戚鲁（华东师范大学）
题目：Stable degeneration of Fano fibrations and birational geometry
摘要：Fano fibrations can be viewed as an interpolation between Fano varieties and klt singularities, for which MMP type contractions are also important examples. In this talk, we discuss the interaction between stable degeneration for Fano fibrations and bitational geometry. In one direction, based on boundedness of complements and higher rank finite generation, we prove the stable degeneration for Fano fibration germs, recently conjectured by Sun-Zhang. In the other direction, we prove some boundedness results of Fano fibrations, with applications in the minimal model program. The major input includes the stable degeneration of singularities, a local-global principle for volumes, and a boundedness argument involving Syzygies. Based on a series of ongoing work joint with Jingjun Han, Jiyuan Han, Minghao Miao, Linsheng Wang, Tong Zhang and Ziquan Zhuang.
吴小行（武汉科技大学）
题目：On adjoint divisors for foliated surfaces
摘要：we will characterize the structure of the negative part of the Zariski decomposition of K_F+D for a foliated surface (X,F) associated with a Q-divisor D whenever K_F + D is pseudoeffective. As applications, we will study the effective behavior of the multiple linear system |m(K_F +D)| for any sufficiently divisible integer m > 0. This is based on joint work with Lu Jun and Xu Shi.
