Title: Displaying the cohomology of toric line bundles
Abstract:Abstract There is a standard approach to calculate the cohomology of torus-invariant sheaves <?CDATA $\mathcal{L}$?> on a toric variety via the simplicial cohomology of the associated subsets <?CDATA ...Abstract There is a standard approach to calculate the cohomology of torus-invariant sheaves <?CDATA $\mathcal{L}$?> on a toric variety via the simplicial cohomology of the associated subsets <?CDATA $V(\mathcal{L})$?> of the space <?CDATA $N_\mathbb{R}$?> of 1-parameter subgroups of the torus. For a line bundle <?CDATA $\mathcal{L}$?> represented by a formal difference <?CDATA $\Delta^+-\Delta^-$?> of polyhedra in the character space <?CDATA $M_\mathbb{R}$?> , [1] contains a simpler formula for the cohomology of <?CDATA $\mathcal{L}$?> , replacing <?CDATA $V(\mathcal{L})$?> by the set-theoretic difference <?CDATA $\Delta^- \setminus \Delta^+$?> . Here, we provide a short and direct proof of this formula.Read More