Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A characterization of projective space via lengths of extremal rays

Osamu Fujino, Eric Jovinelly, Brian Lehmann, Eric Riedl

Abstract

We prove a new characterization of complex projective space using lengths of extremal rays.

A characterization of projective space via lengths of extremal rays

Abstract

We prove a new characterization of complex projective space using lengths of extremal rays.
Paper Structure (5 sections, 10 theorems, 42 equations)

This paper contains 5 sections, 10 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Extremal rays for quasi-log schemes
  3. A Characterization of Projective Space
  4. Terminal varieties
  5. General case

Key Result

Theorem 1.1

Let $X$ be an $n$-dimensional projective variety and let $\Delta$ be an effective $\mathbb{R}$-divisor on $X$ such that $K_X+\Delta$ is $\mathbb{R}$-Cartier. Assume that there exists a $(K_X+\Delta)$-negative extremal ray which is rational, relatively ample at infinity, and satisfies Then $X\simeq \mathbb P^n$, $(X,\Delta)$ is terminal, and $\Delta$ is a divisor of degree less than $1$.

Theorems & Definitions (23)

  • Theorem 1.1
  • Corollary 1.2
  • Corollary 1.3
  • Remark 1.4
  • Theorem 2.1: fujino6
  • proof
  • Theorem 2.2: Lengths of extremal rational curves, fujino6
  • proof
  • Corollary 2.3: fujino6
  • proof
  • ...and 13 more