# Mathematical Science Workshop in Algebraic Geometry

Events

## Schedule

• 8:50 Opening
• 9:00 - 10:00 Shramov
• 10:15 - 11:15 Gong
• 11:30 - 13:00 Lunch and discussion
• 13:30 - 14:30 Yu
• 14:45 - 15:45 Xu
• 16:00 - 17:00 Gu

## Details

### 9:00 - 10:00

#### Speaker

Constantin Shramov
Steklov Mathematical Institute and NRU HSE, Moscow

• Title: Jordan property for birational automorphism groups
• Abstract: I will survey various boundedness results for finite groups acting by (birational) automorphisms of algebraic varieties. I will mainly focus on a so called Jordan property, which holds for large classes of varieties, and also on several particular situations when stronger results can be obtained.

### 10:15 - 11:15

#### Speaker

Cheng Gong
School of Mathematical Sciences, Soochow University

• Title: Classification of families of curves with small number of singular fibers
• Abstract: A relatively minimal family of curves $f: S\rightarrow \mathbb{P}^1$ with 2 or 3 singular fibers is called a Belyi family or fibration, which has some interesting arithmetic and geometric properties. We classify all Belyi families $f$ of curves of genus $g \geq 2$ with two singular fibers. We compute all sections of $f$ and its Mordell-Weil group. As an application, we prove that any periodic fiber can be realized as a fiber of a Belyi fibration with two singular fibers. In this talk, we also discuss some new results over a field of positive characteristic.

### 13:30 - 14:30

#### Speaker

Xun Yu
Centre for Applied Mathematics, Tianjin University

• Title: Minimum positive entropy of complex Enriques surface automorphisms
• Abstract: We determine the minimum positive entropy of complex Enriques surface automorphisms. This together with McMullen's work completes the determination of the minimum positive entropy of complex surface automorphisms in each class of Enriques-Kodaira classification of complex surfaces. As in McMullen's work, we finally reduce the problem to computer algebra. In this talk, after recalling known results and differences from Enriques case, I would like to explain how one can reduce this problem to finite computational problems which can be done by computer. This is a joint work with Professor Keiji Oguiso.

### 14:45 - 15:45

#### Speaker

Ze Xu
School of Mathematics, Shandong University

• Title: Algebraic Cycles on a Generalized Kummer Variety
• Abstract: We compute explicitly the Chow motive of any generalized Kummer variety associated to any abelian surface. In fact, it lies in the rigid tensor subcategory of the category of Chow motives generated by the Chow motive of the underlying abelian surface. One application of this calculation is to show that the Hodge conjecture holds for arbitrary products of generalized Kummer varieties. As another application, all numerically trivial 1-cycles on arbitrary products of generalized Kummer varieties are smashnilpotent.

### 16:00 - 17:00

#### Speaker

Yi Gu
School of Mathematical Sciences, Soochow University

• Title: Number of singular fibres for surfaces fibrations over P^1 in positive characteristics
• Abstract: After Gong’s talk, we will continue to discuss the lower bound for the number of singular fibres for a relatively minimal surface fibration f: X->P^1 satisfying various prescribed properties in almost all positive characteristics.