35th Autumn School in Algebraic Geometry

Subgroups of Cremona groups

Lukecin, Poland, September 23 -- September 29, 2012

Teachers: Jeremy Blanc (Basel) and Yuri Prokhorov (Moscow)

Abstract: The subject of the school concerns finite subgroups of groups of birational transformations of projective spaces. This topic is classical and goes back to the last quarter of the 19th century and it has its vivid renaissance in the last two decades. Two series of lectures will survey the most recent methods and results in this field. The lectures of Yuri Prokhorov will focus on Fano manifolds and will provide an introduction to Mori theory. The lectures of Jeremy Blanc will concentrate on finite subgroups of birational transformations of the plane.

Prerequisites: Basic knowledge of algebraic geometry.

Program of the school: There will be 2 lectures each morning, 90 min each, followed by 90 min excercise session in the afternoon and contributed talks in the evening.

Fano varieties and Cremona groups, by Yuri Prokhorov.

Abstract (subject to change): The aim of this course is to present basic results on Fano varieties and give examples; it will also serve as a preparation for the course of Jeremy Blanc. The following topics will be covered:

Readings to Prokhorov's lectures:

Finite subgroups of the Cremona group in dimension 2, by Jeremy Blanc.

Abstract: This course will be devoted to the study of finite subgroups of the Cremona group in dimension 2. This is closely related to the G-equivariant MMP in dimension 2, which has the advantage to be really easier than in dimensions higher (and in fact proved far before Mori statements). The course will describe the geometry on del Pezzo surfaces and conic bundles with a group action, and relation between all these models. If time permits, the case of non-algebraically closed field will also be investigated.

Readings to lectures by Blanc.

Organizers: Jaroslaw Buczynski, Jaroslaw Wisniewski, Institute of Mathematics, Warsaw University.

The joint picture of participants

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