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PreprintCC BY 4.0arXiv

K-regularity for finite quotient singularities

  • Matthew Satriano
  • Wanchun Shen
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Abstract

We study K-regularity for complex varieties with finite quotient singularities. We prove that for such varieties, K1-regularity is equivalent to smoothness whenever the singular locus is contained in an affine closed subvariety (e.g., affine varieties or those with isolated singularities). In contrast, we construct projective varieties with finite quotient singularities which are Km-regular for every m but are not local complete intersections. Our smoothness criterion is obtained by affirmatively answering Fogarty's 1988 question concerning differential forms on finite quotients.

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Cite

BibTeXRIS
BibTeX
@misc{satriano2026kregularity,
  title = {{$K$-regularity for finite quotient singularities}},
  author = {Matthew Satriano and Wanchun Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21043},
  eprint = {2609.21043},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21043},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - K-regularity for finite quotient singularities
AU  - Matthew Satriano
AU  - Wanchun Shen
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.21043
UR  - https://arxiv.org/abs/2609.21043
AB  - We study K-regularity for complex varieties with finite quotient singularities. We prove that for such varieties, K_1-regularity is equivalent to smoothness whenever the singular locus is contained in an affine closed subvariety (e.g., affine varieties or those with isolated singularities). In contrast, we construct projective varieties with finite quotient singularities which are K_m-regular for every m but are not local complete intersections. Our smoothness criterion is obtained by affirmatively answering Fogarty's 1988 question concerning differential forms on finite quotients.
ER  -