Details
| Original language | English |
|---|---|
| Pages (from-to) | 683-693 |
| Number of pages | 11 |
| Journal | Izvestiya mathematics |
| Volume | 84 |
| Issue number | 4 |
| Publication status | Published - 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.
Keywords
- Cartier divisor, lattice, line bundle, polytope, sheaf cohomology, toric variety
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Izvestiya mathematics, Vol. 84, No. 4, 08.2020, p. 683-693.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Displaying the cohomology of toric line bundles
AU - Altmann, K.
AU - Ploog, David
PY - 2020/8
Y1 - 2020/8
N2 - 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.
AB - 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.
KW - Cartier divisor
KW - lattice
KW - line bundle
KW - polytope
KW - sheaf cohomology
KW - toric variety
UR - http://www.scopus.com/inward/record.url?scp=85092255301&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1903.08009
DO - 10.48550/arXiv.1903.08009
M3 - Article
AN - SCOPUS:85092255301
VL - 84
SP - 683
EP - 693
JO - Izvestiya mathematics
JF - Izvestiya mathematics
SN - 1064-5632
IS - 4
ER -