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Horospherical varieties with quotient singularities

Sean Monahan

Abstract

Our main result is a combinatorial characterization of when a horospherical variety has (at worst) quotient singularities. Using this characterization, we show that every quasiprojective horospherical variety with quotient singularities is globally the quotient of a smooth variety by a finite abelian group.

Horospherical varieties with quotient singularities

Abstract

Our main result is a combinatorial characterization of when a horospherical variety has (at worst) quotient singularities. Using this characterization, we show that every quasiprojective horospherical variety with quotient singularities is globally the quotient of a smooth variety by a finite abelian group.

Paper Structure

This paper contains 9 sections, 5 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Characterization of quotient singularities
  3. Open questions
  4. Fixed notation
  5. Preliminaries
  6. Affine local structure
  7. Cox construction
  8. Vividness
  9. Main results

Key Result

theorem 1.2

fulton's question has an affirmative answer for any quasiprojective horospherical variety $X$ with quotient singularities. In fact, $F$ may be taken to be a finite diagonalizable (hence abelian) group.

Theorems & Definitions (21)

  • theorem 1.2: Fulton's question for horospherical varieties
  • remark 1.3
  • definition 1.4: Simplicial/regular
  • definition 1.5: Vivid
  • theorem 1.5: Characterization of quotient singularities
  • remark 1.6
  • remark 2.3: Cox construction with torus factors
  • definition 2.3: Vivid
  • remark 2.4
  • example 2.5: cf. pasquier2006thesis
  • ...and 11 more