Conference in birational geometry (USTC 2024)

Time:  September 20-23 (registration on the 19th)

Room: C Building, Room C1124, Material Science Research Building (物质科研楼C座1124，科大东区)

Accommodation:Jiangnanchun Hotel（江南春）

Organizers:  LeiZhang,Junchao Shentu

Contact :  Lei Zhang( zhlei18@ustc.edu.cn, 13572098164)

Schedule

Invited Speakers：

Titles and abstracts

Paolo Cascini

Title: Foliation Adjunction.

Abstract: We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of foliation singularities. Joint work with C. Spicer.

Fabrizo Catanese

Title: Quasi-etale maps, orbifolds, and characterizations of quotients of tori and  bounded symmetric domains.

Abstract: I will begin by recalling an older result of mine:  two Kaehler surfaces have the same Kodaira dimension if and only if they are equivalent by the QED equivalence, generated by quasi-etale maps and deformations.

In higher dimensions, some characterization of quotients follow in an easier way by considering orbifolds, Deligne Mostow orbifolds, or more general ones. I will illustrate 2 recent results concerning 

1. the characterization of quotients of complex tori as Kaehler orbifold classifying spaces for even crystallographic groups 

2. the characterization of  quotient orbifolds of bounded symmetric domains of tube type.

Chen Jiang

Title: Characterization of canonical threefolds with small genera and minimal volumes

Abstract: For a smooth projective threefold of general type with geometric genus 2, it is known that its canonical volume is at lease 1/3. We will give a characterization of the equality case. It turns out that the canonical model of such a 3-fold must be a hypersurface of degree 16 in the weighted projective space P(1,1,2,3,8),  which gives an explicit description of its canonical ring. This implies that the coarse moduli space parametrizing all canonical $3$-folds with canonical volume 1/3 and geometric genus 2, is an irreducible variety of dimension 189. This is a joint work with Meng Chen and Yong Hu.

Yujiro Kawamata

Title: On NC deformations of smooth varieties.

Abstract: I will explain a general theory of infinitesimal and formal NC deformations of smooth varieties.  

Then I will prove that the derived McKay correspondence between the commutative and NC crepant resolutions for a surface singularity of type A extends under NC deformations.

Yongnam Lee

Title: Compact moduli of elliptic surfaces with a multi-section

Abstract: Motivated by Miranda and Ascher-Bejleri's works on compactification of moduli space of rational elliptic surfaces with a section, we study to construct compacti moduli space of elliptic surfaces with a multi-section. Particular emphasis is placed on the study of rational elliptic surfaces without section and Dolgachev surfaces. The main approach to understanding limit surfaces is Q-Gorenstein smoothing of slc surfaces. This is a joint work with Donggun Lee.

Sheng Meng

Title: On surjective endomorphisms of projective varieties.

Abstract: Let X be a normal projective variety over C. Let f be a surjective endomorphism of X. In this talk, I will try to explain our current program on the classification and the building blocks of (f,X), involving two main tools: equivariant minimal model program and dynamical Iitaka fibration. In this talk, I will focus on its application to the Kawaguchi-Silverman conjecture, which asserts the equality of the arithmetic degree and the first dynamical degree for points of Zariski dense orbit. This is based on several joint works with Guolei Zhong and De-Qi Zhang.

Keiji Oguiso

Title: Elliptically fibered Calabi-Yau threefold with a relative birational automorphism of positive algebraic entropy

Abstract: I would like to present, with relevant results and open problems, a fairly concrete structure theorem of elliptically fibered Calabi-Yau threefolds with a birational automorphism of first dynamical degree > 1, preserving the fibration.

Xun Yu

Title: On automorphism groups of smooth hypersurfaces

Abstract: We show that smooth hypersurfaces in complex projective spaces with automorphism groups of maximum size are isomorphic to Fermat hypersurfaces, with a few (explicitly given) exceptions. This is a joint work with Song Yang and Zigang Zhu.

Deqi Zhang

Title:The Equivariant Minimal Model Program and its Applications to Algebraic and Arithmetic Dynamics

Abstract: We report our recent progress on the Equivariant Minimal Model Program (EMMP), the MMP which preserves an endomorphism f of a projective variety with mild singularities. We apply this EMMP to algebraic and arithmetic dynamics, especially to the Kawaguchi-Silverman conjecture (KSC) about the equality of dynamical degree and arithmetic degree of f, and the Zariski Dense Orbit conjecture (ZDO) of f.