Displaying the cohomology of toric line bundles
- 作者: Altmann K.1, Ploog D.2
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隶属关系:
- Freie Universität Berlin, Institut für Mathematik
- Universität Hannover, Institut für Mathematik
- 期: 卷 84, 编号 4 (2020)
- 页面: 66-78
- 栏目: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/142293
- DOI: https://doi.org/10.4213/im8948
- ID: 142293
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详细
There is a standard approach to calculate the cohomology of torus-invariant sheaves$\mathcal{L}$ on a toric variety via the simplicial cohomology of the associated subsets$V(\mathcal{L})$ of the space $N_\mathbb{R}$ of 1-parameter subgroups of the torus.For a line bundle $\mathcal{L}$ represented by a formal difference $\Delta^+-\Delta^-$ of polyhedrain the character space $M_\mathbb{R}$, [1] contains a simpler formula for the cohomology of $\mathcal{L}$, replacing $V(\mathcal{L})$ by the set-theoretic difference $\Delta^- \setminus \Delta^+$.Here, we provide a short and direct proof of this formula.
作者简介
Klaus Altmann
Freie Universität Berlin, Institut für Mathematik
Email: izv@mi-ras.ru
David Ploog
Universität Hannover, Institut für Mathematik
编辑信件的主要联系方式.
Email: izv@mi-ras.ru
Doctor of physico-mathematical sciences
参考
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