Number Theory Seminar

Luigi Lombardi (Bonn)

Title: Deformations of minimal cohomology classes and regularity.

Abstract: In this talk I will present a conjecture of Debarre, Pareschi and Popa on the classification and characterization of subvarieties of abelian varieties representing a minimal cohomology class. I will discuss an approach via deformation theory to give a further evidence to the conjecture. In the second part of the talk I will establish a regularity bound called Theta-regularity for ideal sheaves of curves embedded in abelian varieties. This is a further step towards the conjecture mentioned above as Theta-regularity should characterize minimal cohomology classes as those having the least possible regularity.