**Beijing Algebraic Geometry Colloquium**12th Meeting

November 3, 2018

Room 77201, BICMR, PKU

**Algebraic Geometry Activities in China**Matteo Ruggiero

(Paris Diderot)

Algebraically stable models for holomorphic maps on normal surface singularities

14:00 - 15:00

Let f be a holomorphic selfmap of a normal surface singularity (X, x_0), and let π: X_π -> (X, x_0) be a proper birational map. We say that the lift f_π of f on X_π is algebraically stable if for every compact curve E in X_π, its image through high iterates of f_π does not belong to the indeterminacy set of f_π. In joint work with William Gignac, we show that for any proper birational map π', there exists a higher model π for which f_π is algebraically stable, but for one class of exceptions, where such models do not exist. The proof relies on the study of the action f_* induced by f on a suitable space of valuations V, following techniques previously introduced by Charles Favre and Mattias Jonsson. In our setting, we construct a distance on V for which f_* is non-expanding. This allows to deduce fixed point theorems for f_*.

Chen Jiang

(Kavli IPMU)

Anti-canonical geometry of Fano 3-folds

15:20 - 16:20

We are interested in the explicit geometry of Fano 3-folds given by the pluri-anti-canonical systems. For a Q-factorial terminal Fano 3-fold of Picard number 1, we show that the 39-th pluri-anti-canonical map is birational onto its image. For a canonical weak Fano 3-fold, we show that the 97-th pluri-anti-canonical map is birational, and the 52-nd pluri-anti-canonical map is birational if changed by a birational model. I will explain some ideas of the proof and further applications. This talk is based on joint work with Meng Chen.

Junwu Tu

(ShanghaiTech)

Categorical Saito theory

16:40 - 17:40

In this talk, I shall present a categorical construction of Saito's theory of primitive forms. The key observation is to use Kontsevich/Tsygan formality to study the category of matrix factorizations. Indeed, as an application of this new technology, we prove a comparison result that the categorical construction is equivalent to Saito's original one, through a kind of B-model open-closed map. Joint work with Andrei Căldăraru.

**Organized by****Baohua Fu**CAS**Lei Fu**Tsinghua**Xiaotao Sun**CAS**Zhiyu Tian**PKU**Qizheng Yin**PKU**Past Meetings**

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AG Activities in China

Algebraic geometry activities in Beijing and throughout China.

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