Orbifold Slope Rational-Connectedness

TL;DR

This paper introduces the concept of slope rational connectedness for smooth orbifold pairs, characterizes it through various geometric conditions, and constructs the orbifold rational quotient map, extending classical ideas to orbifolds.

Contribution

It defines slope rational connectedness for orbifolds, establishes equivalent characterizations, and constructs the orbifold rational quotient map, advancing the understanding of orbifold geometry.

Findings

Characterization of orbifold slope rational connectedness

Construction of the orbifold rational quotient map

Extension of rational connectedness concepts to orbifolds

Abstract

The notion of 'slope rational connectedness' is introduced in the context of smooth orbifold pairs. The main result parallels the characterization of the rational connectedness of projective manifolds in terms of either the non-existence of holomorphic covariant tensors, or of absence of fibrations onto manifolds with pseudo-effective canonical bundle, or of existence of movable classes for which the minimal slope of the tangent bundle is positive. We then use this result to construct the `rational quotient map' in orbifold category.