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Discrepancies of $p$-cyclic quotient varieties

Takehiko Yasuda

Abstract

We consider the quotient variety associated to a linear representation of the cyclic group of order p in characteristic p>0. We estimate the minimal discrepancy of exceptional divisors over the singular locus. In particular, we give criteria for the quotient variety being terminal, canonical and log canonical. As an application, we obtain new examples of non-Cohen-Macaulay terminal singularities, adding to examples recently announced by Totaro.

Discrepancies of $p$-cyclic quotient varieties

Abstract

We consider the quotient variety associated to a linear representation of the cyclic group of order p in characteristic p>0. We estimate the minimal discrepancy of exceptional divisors over the singular locus. In particular, we give criteria for the quotient variety being terminal, canonical and log canonical. As an application, we obtain new examples of non-Cohen-Macaulay terminal singularities, adding to examples recently announced by Totaro.

Paper Structure

This paper contains 3 sections, 11 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Motivic integration
  3. Proof of Theorems \ref{['thm:precise']} and \ref{['thm:log-term']}

Key Result

Theorem 1.1

If $D_{V}\ge p$, then $X$ is canonical.

Theorems & Definitions (21)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Corollary 1.4
  • Proposition 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • ...and 11 more