Displaying the cohomology of toric line bundles

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • K. Altmann
  • David Ploog

Organisationseinheiten

Externe Organisationen

  • Freie Universität Berlin (FU Berlin)
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Details

OriginalspracheEnglisch
Seiten (von - bis)683-693
Seitenumfang11
FachzeitschriftIzvestiya mathematics
Jahrgang84
Ausgabenummer4
PublikationsstatusVeröffentlicht - Aug. 2020

Abstract

There is a standard approach to calculate the cohomology of torus-invariant sheaves Ⅎ on a toric variety via the simplicial cohomology of the associated subsets V(Ⅎ) of the space Nℝ of 1-parameter subgroups of the torus. For a line bundle Ⅎ represented by a formal difference Δ+ - Δ- of polyhedra in the character space Mℝ, [1] contains a simpler formula for the cohomology of Ⅎ, replacing V(Ⅎ) by the set-theoretic difference Δ-\Δ+. Here, we provide a short and direct proof of this formula.

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Displaying the cohomology of toric line bundles. / Altmann, K.; Ploog, David.
in: Izvestiya mathematics, Jahrgang 84, Nr. 4, 08.2020, S. 683-693.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Altmann K, Ploog D. Displaying the cohomology of toric line bundles. Izvestiya mathematics. 2020 Aug;84(4):683-693. doi: 10.48550/arXiv.1903.08009, 10.1070/IM8948
Altmann, K. ; Ploog, David. / Displaying the cohomology of toric line bundles. in: Izvestiya mathematics. 2020 ; Jahrgang 84, Nr. 4. S. 683-693.
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