# Online Seminar in Algebraic Geometry

## Upcoming talks:

• Time: 13:30 - 14:30, July 30, 2020

Venue: Tencent Meeting ID: 440 891 439

Title: Two counterexamples stemming from Raynaud's surfaces

Speaker: Lei Zhang (University of Science and Technology of China)

Abstract: Subadditivity of Kodaira dimensions and adjoint linear system are two classical problems in the classification of varieties. Concerning the two problems in characteristic $p$, for a long time, we have the same expectations as in characteristic zero, namely, the so called Iitaka conjecture and Fujita conjecture. But we constructed counterexamples last year, which stem from the construction of Raynaud's surfaces. In this talk, we will talk about our examples and propose reasonable expectations. These are joint work with Y. Gu, Y. Zhang, P. Cascini, S. Ejiri and J. Kollar.

## Past talks:

• Time: 16:00 - 17:00, July 23, 2020

Venue: Tencent Meeting

Title: Quillen metric, BCOV invariant and motivic integration

Speaker: Yeping Zhang (Korea Institute for Advanced Study)

Abstract: Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called the BCOV invariant. The BCOV invariant is conjecturally related to the Gromov-Witten theory via mirror symmetry. In this talk, we prove the conjecture that birational Calabi-Yau manifolds have the same BCOV invariant. We also build an analogue between the BCOV invariant and the motivic integration. The result presented in this talk is a joint work with Lie Fu.

• Time: 13:30 - 14:40, June 11, 2020

Venue: Tencent Meeting

Title: Stability conditions and Fujita's conjecture

Speaker: Hao Sun (Shanghai Normal University)

Abstract: We will introduce the definition of Bridgeland stability conditions and the recent progress on the construction of Bridgeland stability conditions on projective threefolds with vanishing Chern classes. The application to Fujita's conjecture will also be discussed.

• Time: 15:00 - 16:00, May 29, 2020

Venue: Tencent Meeting

Title: $n$ dimensional Minimal models with Kodaira dimension $n-1$ and trivial $c_1^{n-2}c_2$

Speaker: Feng Hao (Katholieke Universiteit Leuven)

Abstract: In this talk, I will give a classification of minimal models of dimension $n$, Kodaira dimension $n-1$ and trivial $c_1^{n-2}c_2$, which is a question proposed by Kollar in dimension three. Also, I will show for minimal threefolds, $c_1c_2$ are either $0$ or universally bounded away from $0$. This is a joint work with Stefan Schreieder.

• Time: 13:30 - 14:30, May 7, 2020

Venue: Tencent Meeting

Title: Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Speaker: Wenhao Ou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Abstract: If $X$ is a projective manifold whose tangent bundle $T_X$ contains a strictly nef locally free subsheaf, we prove that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. This is joint with Jie Liu and Xiaokui Yang.

• Time: 13:30 - 14:30, April 30, 2020

Venue: Tencent Meeting

Title: Finite $p$-groups of birational automorphisms and a characterization of rational varieties

Speaker: Jinsong Xu (Xi'an Jiaotong Liverpool University)

Abstract: We study finite $p$-subgroups of birational automorphism groups. We prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an algebraically closed field is rational if its birational automorphism group contains a $p$-subgroups of maximal rank for $p>R(n)$. We will also discuss some related questions on finite $p$-groups.