Displaying the cohomology of toric line bundles

2019/03/19 by Altmann, Klaus, Ploog, David · 1 citation
#14C20 #14F05 #14M25 #52B20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.08009

Abstract

There is a standard method to calculate the cohomology of torus-invariant sheaves L on a toric variety via the simplicial cohomology of associated subsets V(L) of the space N_{\mathbb R} of 1-parameter subgroups of the torus. For a line bundle L represented by a formal difference Δ⁺-Δ^- of polyhedra in the character space M_{\mathbb R}, [ABKW18] contains a simpler formula for the cohomology of L, replacing V(L) by the set-theoretic difference Δ^- ∖ Δ⁺. Here, we provide a short and direct proof of this formula.

Cited by

• Acyclic toric sheaves

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