PreprintCC BY 4.0arXiv
Elementary transformations of toric vector bundles
Abstract
We describe negative and positive elementary transformations of toric vector bundles in terms of Klyachko filtrations. We first determine the filtrations of the restriction of a toric vector bundle to an invariant prime divisor and then derive explicit formulas for the transformed bundle: only the filtration at the distinguished ray changes. As applications, we interpret adding and removing invariant boundary components of logarithmic tangent bundles as elementary transformations and recover the residue sequence for logarithmic cotangent bundles.
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BibTeX
@misc{huh2026elementary,
title = {{Elementary transformations of toric vector bundles}},
author = {Sukmoon Huh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34885},
eprint = {2610.34885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34885},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elementary transformations of toric vector bundles
AU - Sukmoon Huh
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34885
UR - https://arxiv.org/abs/2610.34885
AB - We describe negative and positive elementary transformations of toric vector bundles in terms of Klyachko filtrations. We first determine the filtrations of the restriction of a toric vector bundle to an invariant prime divisor and then derive explicit formulas for the transformed bundle: only the filtration at the distinguished ray changes. As applications, we interpret adding and removing invariant boundary components of logarithmic tangent bundles as elementary transformations and recover the residue sequence for logarithmic cotangent bundles.
ER -