Beschränkte Familien kohärenter Garben auf Kähler-Mannigfaltigkeiten
Friday, 1.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Lagrangian fibrations on hyperkähler manifolds
Friday, 8.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Hyperkähler (also called irreducible holomorphic symplectic) manifolds form an important class of manifolds with trivial canonical bundle. One fundamental aspect of their structure theory is the question whether a given hyperkähler manifold admits a Lagrangian fibration. I\nwill report on a joint project with Christian Lehn and Sönke Rollenske investigating the following question of Beauville: if a hyperkähler manifold contains a complex torus T as a Lagrangian submanifold, does it\nadmit a (meromorphic) Lagrangian fibration with fibre T ?
TBA
Friday, 8.7.11, 10:15-11:15, Raum 404, Eckerstr. 1
Sharp bounds on the denominators of the moduli part in the canonical bundle formula
Friday, 15.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
The canonical bundle formula for a fibration f from (X,B)\nto Y consists in writing KX+B as the pullback of a sum of\nQ-divisors on Y, more precisely KX+B is the pullback of KY+D+M where KY is the canonical divisor, D contains some informations on the singular fibres and M is called moduli part.\n\nIt has been conjectured by Prokhorov and Shokurov that if\nthe fibres of f are curves then 12rM is base point free, where r is the Cartier index of the fibre. The conjecture in particular implies that 12rM has integer coefficients.\nIn this talk we will give a counterexample to the conjecture and we will give a sharp bound depending on r for the integer m such that mM has integer coefficients.
TBA
Friday, 22.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Ein Vergleich lokal analytischer Gruppenkohomologie mit Lie algebren Kohomologie für p-adische Lie Gruppen
Wednesday, 27.7.11, 14:00-15:00, Raum 404, Eckerstr. 1
Calculating the arithmetic volume of certain Shimura varieties using Borcherds theory.
Friday, 29.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
The talk will be about the verification of parts of Kudla's\nconjectures on arithmetic theta functions, in particular of\ntheir relation to derivatives of Eisenstein series in\narbitrary dimensions. This approach uses an extended Arakelov theory, the theory of Borcherds products, and a functorial theory of integral canonical models of toroidal compactifications of Shimura varieties. Kudla's conjectures arose to conceptually understand the mechanism in Gross- and Zagier's approach to the Birch and Swinnerton-Dyer conjecture.