Campana separable rational connectedness of toric orbifold

TL;DR

This paper proves that smooth non-klt toric orbifolds are separably Campana rationally connected, extending previous results, and demonstrates the existence of positive characteristic cases where certain orbifolds are not separably Campana rationally connected.

Contribution

It extends the known results on Campana rational connectedness from klt to non-klt toric orbifolds and explores characteristic-dependent properties of weighted projective spaces.

Findings

Smooth non-klt toric orbifolds are separably Campana rationally connected.

Existence of positive characteristic where non-klt weighted projective spaces are not separably Campana rationally connected.

Extension of Campana rational connectedness results to non-klt cases.

Abstract

We prove that smooth non-klt toric orbifolds are separably Campana rationally connected, extending the result in the klt case. We also show that there always exists a positive characteristic in which a singular weighted projective space, viewed as a non-klt Campana orbifold, is not separably Campana rationally connected.