Cartier and Weil Divisors on Varieties with Quotient Singularities

TL;DR

This paper demonstrates that Weil and Cartier $Q$-divisors are equivalent on $V$-manifolds and provides a method to convert rational Weil divisors into Cartier divisors, with applications to weighted projective spaces.

Contribution

It establishes the equivalence of Weil and Cartier $Q$-divisors on $V$-manifolds and introduces a procedure for expressing rational Weil divisors as Cartier divisors.

Findings

Weil and Cartier $Q$-divisors coincide on $V$-manifolds.

A method to express rational Weil divisors as Cartier divisors is provided.

Applications are demonstrated on weighted projective spaces and blow-ups.

Abstract

The main goal of this paper is to show that the notions of Weil and Cartier $\mathbb{Q}$-divisors coincide for $V$-manifolds and give a procedure to express a rational Weil divisor as a rational Cartier divisor. The theory is illustrated on weighted projective spaces and weighted blow-ups.