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 2.009 (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: To be announced

Abstract: To be announced.
05.11.2014 kein Seminar


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