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

Abstract

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.

31 pages, 11 figures

Cited by in corpus (2)

• Functorial embedded resolution via weighted blowings up
• Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting