Geometry Seminar
University of Tor Vergata, Department of Mathematics
15th of April 2025, 14:30-16:00,room D’Antoni
Semi-homogeneous vector bundles and cohomological rank functions on abelian varieties
Nelson René Alvarado
Università di Roma Tor Vergata
In this talk we discuss semi-homogeneous vector bundles on abelian varieties and show that, from a cohomological point of view, they play the role that fractional polarizations should play. In the first part of the seminar we discuss some Mukai's results regarding the existence and structure of semi-homogeneous bundles. In the second part we revisit the theory of cohomological rank functions giving a vector bundle interpretation of them. As an application, we show how this perspective allows us to bound certain numerical invariants that measure the positivity of polarizations. |