Chi-y genera of generic intersections in algebraic tori and refined tropicalizations

Algebra Seminar
Friday, October 26, 2018 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Andreas Gross – Colorado State University
Philipp Jell
An algorithm to compute chi-y genera of generic complete intersections in algebraic tori has already been known since the work of Danilov and Khovanskii in 1978, yet a closed formula has been given only very recently by Di Rocco, Haase, and Nill. In my talk, I will show how this formula simplifies considerably after an extension of scalars. I will give an algebraic explanation for this phenomenon using the Grothendieck rings of vector bundles on toric varieties. We will then see how the tropical Chern character gives rise to a refined tropicalization, which retains the good properties of the usual, unrefined tropicalization.