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Holomorphic polyvector fields on toric varieties via Klyachko filtrations
Abstract
Motivated by the extended deformation theory of complex manifolds, we give a combinatorial description of holomorphic polyvector fields on a smooth compact toric variety via Klyachko's filtrations. This yields dimension and formal equivariant-character formulas and recovers the descriptions of Demazure roots and anticanonical sections.
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BibTeX
@misc{hong2026holomorphic,
title = {{Holomorphic polyvector fields on toric varieties via Klyachko filtrations}},
author = {Wei Hong and Maosong Xiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14315},
eprint = {2609.14315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14315},
}
RIS
TY - UNPB
TI - Holomorphic polyvector fields on toric varieties via Klyachko filtrations
AU - Wei Hong
AU - Maosong Xiang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14315
UR - https://arxiv.org/abs/2609.14315
AB - Motivated by the extended deformation theory of complex manifolds, we give a combinatorial description of holomorphic polyvector fields on a smooth compact toric variety via Klyachko's filtrations. This yields dimension and formal equivariant-character formulas and recovers the descriptions of Demazure roots and anticanonical sections.
ER -