Work

A boundedness theorem for cone singularities

Year: 2025

Type: article

Abstract: A cone singularity is a normal affine variety X with an effective one-dimensional torus action with a unique fixed point $$x\in X$$ x ∈ X which lies in the closure of any orbit of the $$k^*$$ k ∗ -action. In this article, we prove a boundedness theorem for cone singularities in terms of their dimension, singularities, and isotropies. Given d and N two positive integers and $$\epsilon $$ ϵ a positive real number, we prove that the class of d -dimensional $$\epsilon $$ ϵ -log canonical cone singularities with isotropies bounded by N forms a bounded family.

Source: manuscripta mathematica

DOI: 10.1007/s00229-025-01667-2

Author: Joaquín Moraga

Institution: University of California, Los Angeles

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: National Science Foundation