Wintersemester 2011/12

19.10.2011 Igor Dolgachev (Univ. Michigan)

Algebraic surfaces with large automorphism group

Abstract: An automorphism group of a projective algebraic surface acts naturally on the Neron-Severi group of algebraic 2-cycles preserving the intersection form and the canonical class. It is called large if its image G in the group O of isometries of the orthogonal complement of the canonical class is an infinite group of finite index. I will explain a recent result of my joint work with Serge Cantat where we proof that the Picard number of a surface with a large automorphism group is at most 11. In the case of rational surfaces with Picard number at least 11, the image of the automorphism group is contained in a certain reflection subgroup W of infinite index in O. We classify all rational surfaces such that G is of finite index in W. In characteristic 0 they are classically known Coble or Halphen surfaces.

26.10.2011

15.15 Uhr Igor Dolgachev (Univ. Michigan)

Configuration spaces of complex and real spheres

Abstract: I will discuss the GIT-quotients of the product of $m$ copies of a projective space equipped with a nonsingular quadric modulo the orthogonal group of the quadric. A classical isomorphism of this group with the Inversive Group of birational transformations of the projective space of one dimension less allows one to interpret the quotient spaces as configuration spaces of $m$ complex (or real) spheres.

16.30 Uhr Björn Andreas (FU Berlin)

On geometrical problems inspired by string theory

Abstract: String theory provides many fresh ideas for studying geometrical structures on manifolds. Some of them are guided by physical intuition and require a rigorous mathematical analysis and a proof of their existence. In this talk we will give a brief overview on some problems in algebraic and differential geometry which emerge out of string theory when combining information of metrics, submanifolds, and bundles and comment on a recent proof of a conjecture by Witten.

08.02.2012 Yuri Tschinkel (New York University)

On the arithmetic of surfaces

19.10.2011	Igor Dolgachev (Univ. Michigan)
	Algebraic surfaces with large automorphism group
	Abstract: An automorphism group of a projective algebraic surface acts naturally on the Neron-Severi group of algebraic 2-cycles preserving the intersection form and the canonical class. It is called large if its image G in the group O of isometries of the orthogonal complement of the canonical class is an infinite group of finite index. I will explain a recent result of my joint work with Serge Cantat where we proof that the Picard number of a surface with a large automorphism group is at most 11. In the case of rational surfaces with Picard number at least 11, the image of the automorphism group is contained in a certain reflection subgroup W of infinite index in O. We classify all rational surfaces such that G is of finite index in W. In characteristic 0 they are classically known Coble or Halphen surfaces.
26.10.2011
15.15 Uhr	Igor Dolgachev (Univ. Michigan)
	Configuration spaces of complex and real spheres
	Abstract: I will discuss the GIT-quotients of the product of $m$ copies of a projective space equipped with a nonsingular quadric modulo the orthogonal group of the quadric. A classical isomorphism of this group with the Inversive Group of birational transformations of the projective space of one dimension less allows one to interpret the quotient spaces as configuration spaces of $m$ complex (or real) spheres.
16.30 Uhr	Björn Andreas (FU Berlin)
	On geometrical problems inspired by string theory
	Abstract: String theory provides many fresh ideas for studying geometrical structures on manifolds. Some of them are guided by physical intuition and require a rigorous mathematical analysis and a proof of their existence. In this talk we will give a brief overview on some problems in algebraic and differential geometry which emerge out of string theory when combining information of metrics, submanifolds, and bundles and comment on a recent proof of a conjecture by Witten.
08.02.2012	Yuri Tschinkel (New York University)
	On the arithmetic of surfaces