19 March 2025 — Verona

Cohomology of toric vector bundles via Weil decorations

Andreas Hochenegger, Politecnico di Milano

Abstract

One can write divisors \(D\) as a difference of two nef divisors. In the toric context, this translates into the formal difference of two polytopes \(P-Q\). It is possible to express the cohomology of \(\mathcal{O}(D)\) via these two polytopes. In my talk I will show how this approach can be generalized to vector bundles \(E\) of higher rank. Using the language of Weil decorations, the cohomology of \(E\) will be related to the cohomology of a constructible sheaf. This is joint work with Klaus Altmann and Frederik Witt.