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.

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures