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** ****Beijing Algebraic Geometry Colloquium**

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**October 17, 2018**

**N913, AMSS**

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**9:30—10:30 ** *Konstantin Shramov* (Steklov Mathematical Institute, Russia)

**Finite groups of birational selfmaps of surfaces**

I will speak about finite groups acting by birational automorphisms of surfaces. In particular, we will consider surfaces over function fields. One of important observations here is that a smooth geometrically rational surface S is either birational to a product of a projective line and a conic (so that S is rational provided that it has a point), or finite subgroups of its birational automorphism group are bounded. I will also discuss some particular types of surfaces with interesting automorphism groups, including Severi-Brauer surfaces.

**10:45—11:45** *Jian Xiao* (Tsinghua Yau Mathematical Sciences Center)

**Local positivity for curves**

One of the most important invariants measuring the local positivity of a nef line bundle is the Seshadri constant. We first give a brief introduction to this invariant. Then using the duality of positive cones, we show that applying the polar transform to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants, studied also independently by M. Fulger, have nice properties similar to those for divisors. In particular, this enables us to obtain a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the non-ample locus of a big class. (Joint work with N. McCleerey.)

Organizers:

Baohua Fu, Lei Fu, Xiaotao Sun, Zhiyu Tian, Qizheng Yin

**Algebraic Geometry Activities in China: ****http://www.alggeom.org/**

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