Humboldt Universität zu Berlin
Mathem.Naturwissenschaftliche Fakultät
Institut für Mathematik
Wintersemester 2014/15
Das Forschungsseminar findet mittwochs in der Zeit von 15:00  17:00 Uhr in der Rudower Chaussee 25, 12489 BerlinAdlershof, 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 BombieriLang conjecture predicts that the krational 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 localglobal 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 α_{x}(L), an invariant measuring the accumulation of rational points around x as gauged by L, and the Seshadri constant ε_{x}(L), measuring the local positivity of L near x. In particular, the classic approximation theorem of K. F. Roth on P^{1} generalizes as an inequality between α_{x} and ε_{x} 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 