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PreprintCC BY 4.0arXiv

Decomposition of toric sheaves

  • Carl Tipler
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Abstract

We show that the abelian category of coherent toric sheaves is generated, as a Serre subcategory, by pushforwards of rank one reflexive sheaves supported on invariant subvarieties. As an application, we extend previous results by Klyachko on cohomology of toric vector bundles to coherent toric sheaves.

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Cite

BibTeXRIS
BibTeX
@misc{tipler2026decomposition,
  title = {{Decomposition of toric sheaves}},
  author = {Carl Tipler},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04603},
  eprint = {2610.04603},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04603},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Decomposition of toric sheaves
AU  - Carl Tipler
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04603
UR  - https://arxiv.org/abs/2610.04603
AB  - We show that the abelian category of coherent toric sheaves is generated, as a Serre subcategory, by pushforwards of rank one reflexive sheaves supported on invariant subvarieties. As an application, we extend previous results by Klyachko on cohomology of toric vector bundles to coherent toric sheaves.
ER  -