Resolutions of linear p-cyclic quotient singularities
Abstract
Let k be an algebraically closed field of positive characteristic p, and let Cp act linearly on a finite-dimensional k-vector space V, with indecomposable Jordan summands Vdi of dimension di. We study projective (crepant) resolutions of V/Cp by constructing a model using the invariant weighted blowup. For V=V2⊕ n, our model is smooth and is the normalization of a blowup of V/Cp. It has a unique exceptional divisor of discrepancy n−p, such that our model is a crepant resolution when n=p. In almost all other cases when the quotient is canonical but not terminal, the invariant weighted blowup model does not produce crepant resolutions, but gives the unique nontrivial projective crepant birational model of the quotient. Consequently, up to trivial summands, we classify the p-cyclic linear quotients admitting a projective crepant resolution.
Related
- Categorical genus for log del Pezzo surfaces with cyclic quotient singularities
- The Kemper--Malle conjecture and isolated linear quotient singularities
- Isolated symplectic singularities admitting symplectic resolutions
- Special Cohen--Macaulay sheaves on partial resolutions of rational surfaces singularities
- Noncommutative resolutions of noncommutative isolated singularities
BibTeX
@misc{fan2026resolutions,
title = {{Resolutions of linear $p$-cyclic quotient singularities}},
author = {Linghu Fan and Hongmin Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07182},
eprint = {2609.07182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07182},
}
RIS
TY - UNPB
TI - Resolutions of linear p-cyclic quotient singularities
AU - Linghu Fan
AU - Hongmin Li
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07182
UR - https://arxiv.org/abs/2609.07182
AB - Let k be an algebraically closed field of positive characteristic p, and let C_p act linearly on a finite-dimensional k-vector space V, with indecomposable Jordan summands V_d_i of dimension d_i. We study projective (crepant) resolutions of V/C_p by constructing a model using the invariant weighted blowup. For V=V_2^⊕ n, our model is smooth and is the normalization of a blowup of V/C_p. It has a unique exceptional divisor of discrepancy n−p, such that our model is a crepant resolution when n=p. In almost all other cases when the quotient is canonical but not terminal, the invariant weighted blowup model does not produce crepant resolutions, but gives the unique nontrivial projective crepant birational model of the quotient. Consequently, up to trivial summands, we classify the p-cyclic linear quotients admitting a projective crepant resolution.
ER -