Humboldt Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Algebraische Geometrie"

Wintersemester 2014/15


Das Forschungsseminar findet mittwochs in der Zeit von 15:00 - 17:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 2.006 (Haus 2, Erdgeschoss), statt.

Seminar: Algebraic Geometry an der FU



15.10.2014 Mike Roth (Queen's University)
Title: Roth’s theorem for arbitrary varieties

Abstract: If X is a variety of general type defined over a number field k, then the Bombieri-Lang conjecture predicts that the k-rational points of X are not Zariski dense. The conjecture is a prediction that a global condition on the canonical bundle (that it is ''generically positive'') implies a global condition about rational points. By the local-global philosophy in geometry we should look for local influence of positivity on the accumulation of rational points. To do that we need measures of both these local phenomena. Let L be an ample line bundle on X, and x an algebraic point. The central theme of the talk is the interrelations between αx(L), an invariant measuring the accumulation of rational points around x as gauged by L, and the Seshadri constant εx(L), measuring the local positivity of L near x. In particular, the classic approximation theorem of K. F. Roth on P1 generalizes as an inequality between αx and εx valid for all projective varieties.
22.10.2014 Thomas Krämer (Universität Heidelberg)
Title: Generic vanishing theory, cubic threefolds and the monodromy of the Gauss map

Abstract: To any closed subvariety of an abelian variety one may attach a reductive algebraic group in a natural way, using the Tannakian formalism. The arising groups are new invariants with interesting applications to the moduli of abelian varieties and the Schottky problem, but their proper geometric interpretation remains mysterious. After a motivated introduction to the Tannakian framework via a generalization of the Green-Lazarsfeld vanishing theorems, I will show that for the theta divisor on the intermediate Jacobian of a smooth cubic threefold the Tannaka group is an exceptional group of type E6. This is the first known exceptional case, and it suggests a surprising connection with the monodromy of the Gauss map and the Fourier-Mukai transform for Higgs bundles.
29.10.2014 Jarod Alper (Australian National University, zzt. HU Berlin)
Title: A Luna etale slice theorem for algebraic stacks

Abstract: Quotient stacks are a distinguished class of algebraic stacks which provide key intuition for studying the geometry of general algebraic stacks. It has long been believed that certain algebraic stacks are in some sense "locally" quotient stacks. In this talk, we will prove that this expectation holds by providing a description of the etale local structure of algebraic stacks near points with linearly reductive stabilizer. We will then discuss a number of striking applications of this result. This is joint work with Jack Hall and David Rydh.
05.11.2014 kein Seminar
19.11.2014 Michael Joswig (TU Berlin)
Title: To be announced

Abstract: To be announced.

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