Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting

Abstract

This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous polynomials of a given degree is derived. This admits an interpretation as a Numerical Adjunction Formula for singular curves on the weighted projective plane.