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.


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