Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting
Algebraic Geometry
2016-09-07 v1 Combinatorics
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.
Cite
@article{arxiv.1506.01168,
title = {Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting},
author = {J. I. Cogolludo-Agustin and J. Martin-Morales and J. Ortigas-Galindo},
journal= {arXiv preprint arXiv:1506.01168},
year = {2016}
}
Comments
18 pages, 2 figures, 1 Table. To appear in Kyoto Journal Of Mathematics