Intersection Theory on Abelian-Quotient $V$-Surfaces and $\mathbf{Q}$-Resolutions

Enrique Artal Bartolo, Jorge Martín-Morales, Jorge Ortigas-Galindo

Published 2011-05-06Version 1

In this paper we study the intersection theory on surfaces with abelian quotient singularities and we derive properties of quotients of weighted projective planes. We also use this theory to study weighted blow-ups in order to construct embedded $\mathbf{Q}$-resolutions of plane curve singularities and abstract $\mathbf{Q}$-resolutions of surfaces.