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PreprintCC BY 4.0arXiv

G0 of complete split toric varieties

  • Zeyu Shen
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Abstract

We compute the Grothendieck group of coherent sheaves for complete split toric surfaces having a smooth 2-dimensional cone in its fan. We show that it is free abelian, of rank equal to the number of rays in the fan. We give a partial generalization of this to all complete split toric varieties.

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Cite

BibTeXRIS
BibTeX
@misc{shen2026complete,
  title = {{$G_0$ of complete split toric varieties}},
  author = {Zeyu Shen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32831},
  eprint = {2610.32831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32831},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - G_0 of complete split toric varieties
AU  - Zeyu Shen
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32831
UR  - https://arxiv.org/abs/2610.32831
AB  - We compute the Grothendieck group of coherent sheaves for complete split toric surfaces having a smooth 2-dimensional cone in its fan. We show that it is free abelian, of rank equal to the number of rays in the fan. We give a partial generalization of this to all complete split toric varieties.
ER  -