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Dimensions of jet schemes of log singularities

Takehiko Yasuda

Abstract

The aim of the paper is to characterize Kawamata log terminal singularities and log canonical singularities by dimensions of jet schemes. It is a generalization of Mustata's result.

Dimensions of jet schemes of log singularities

Abstract

The aim of the paper is to characterize Kawamata log terminal singularities and log canonical singularities by dimensions of jet schemes. It is a generalization of Mustata's result.

Paper Structure

This paper contains 4 sections, 5 theorems, 33 equations.

Table of Contents

  1. Motivic integration
  2. Extended Grothendieck rings of varieties
  3. Jet schemes and motivic measures
  4. Main theorem

Key Result

Lemma 1.3

Assume that $X$ is smooth and $\sum _{i=1}^s D_i$ is a SNC divisor on $X$ with $D_i$ a prime divisor. Let $m_i \in \mathbb Z _{\geq 0}, \ (1 \le i \le s)$, and put $J := \{i| m_i >0 \} \subset \{1, \dots, s\}$. Then we have where

Theorems & Definitions (13)

  • Definition 1.1
  • Definition 1.2
  • Lemma 1.3
  • proof
  • Definition 2.1
  • Theorem 2.2
  • proof
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • ...and 3 more