Cartier and Weil Divisors on Varieties with Quotient Singularities

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.