Cartier and Weil divisors on varieties with quotient singularities

Abstract

It is well-known that the notions of Weil and Cartier Q-divisors coincide for V-manifolds. The main goal of this paper is to give a direct constructive proof of this result providing a procedure to express explicitly a Weil divisor as a rational Cartier divisor. The theory is illustrated on weighted projective spaces and weighted blow-ups.