Overconvergent de Rham-Witt connections
Freitag, 7.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
For a smooth scheme over a perfect field of characteristic p>0, we generalise a definition of Bloch and introduce overconvergent de Rham-Witt connections. This provides a tool to extend the comparison morphisms of Davis, Langer and Zink between overconvergent de Rham-Witt cohomology and Monsky-Washnitzer respectively rigid cohomology to coefficients.\nIn this talk I will describe the main constructions and explain how the comparison theorems can be adapted.
Variation of Moduli Spaces of Gieseker-Maruyama-semistable sheaves
Freitag, 14.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
Moduli spaces of semistable sheaves over polarized projective manifolds of dimensions greater than one have been constructed by Gieseker and Maruyama using Geometric Invariant Theory. In dimension two their variation as the polarization varies has been thoroughly investigated. In dimension three already irrational polarizations appear in an essential way, for which not even the construction of a corresponding moduli space was known. \nIn this talk we present a joint work together with Daniel Greb and Julius Ross in which we introduce and study a new stability notion allowing to solve the construction and variation problems at least in dimension three. The new moduli spaces are obtained as subschemes in moduli spaces of representations of appropriate quivers.
Degenerate flags and Schubert varieties
Freitag, 21.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
Introduced in 2010 by E. Feigin, degenerate flag varieties are degenerations of flag manifolds. It has been proven that, in type A and C, they share many properties with Schubert variety. In this talk I will first recall the classical setting (flag and Schubert varieties) and then discuss joint work with Cerulli Irelli, where we prove a surprising fact about degenerate flags.
Ample subschemes and two conjectures of Hartshorne
Freitag, 28.11.14, 10:15-11:15, Raum 127, Eckerstr. 1
The talk will survey geometric properties of subvarieties and cycles with\nvarious positivity properties. We also discuss related conjectures of\nHartshorne and Peternell about subvarieties with ample normal bundle.