Work

$K$-regularity for finite quotient singularities

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.21043

Authors: Satriano, Matthew, Shen, Wanchun

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Natural Sciences and Engineering Research Council of Canada

OpenAlex ID: W7213939002

Cites: 5

Cited by:

Related to: 10