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A few remarks on effectivity and good minimal models

Vladimir Lazić

Abstract

We prove several results relating the nonvanishing and the existence of good minimal models of different pairs that have the same underlying variety.

A few remarks on effectivity and good minimal models

Abstract

We prove several results relating the nonvanishing and the existence of good minimal models of different pairs that have the same underlying variety.
Paper Structure (3 sections, 11 theorems, 27 equations)

This paper contains 3 sections, 11 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proofs of the main results

Key Result

Theorem 1.1

Assume the existence of good minimal models for projective log canonical pairs in dimensions at most $n-1$. Let $(X,\Delta)$ be a projective log canonical pair of dimension $n$ such that $K_X+\Delta$ is pseudoeffective. Let $G\geq0$ be an $\mathbb{R}$-Cartier $\mathbb{R}$-divisor such that $0\leq\ka Then:

Theorems & Definitions (23)

  • Theorem 1.1
  • Remark 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Corollary 1.5
  • Lemma 2.1
  • proof
  • Corollary 2.2
  • Theorem 2.3
  • proof
  • ...and 13 more