Title: Displaying the cohomology of toric line bundles
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-pa...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 $\Delta^+-\Delta^-$ 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 $\Delta^- \setminus \Delta^+$. Here, we provide a short and direct proof of this formula.Read More
Publication Year: 2019
Publication Date: 2019-03-19
Language: en
Type: preprint
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