Open Access
September 2016 Numerical adjunction formulas for weighted projective planes and lattice point counting
José Ignacio Cogolludo-Agustín, Jorge Martín-Morales, Jorge Ortigas-Galindo
Kyoto J. Math. 56(3): 575-598 (September 2016). DOI: 10.1215/21562261-3600184


This article gives an explicit formula for the Ehrhart quasipolynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasihomogeneous polynomials of a given degree is derived. This admits an interpretation as a numerical adjunction formula for singular curves on the weighted projective plane.


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José Ignacio Cogolludo-Agustín. Jorge Martín-Morales. Jorge Ortigas-Galindo. "Numerical adjunction formulas for weighted projective planes and lattice point counting." Kyoto J. Math. 56 (3) 575 - 598, September 2016.


Received: 22 December 2014; Revised: 14 May 2015; Accepted: 1 June 2015; Published: September 2016
First available in Project Euclid: 22 August 2016

zbMATH: 1353.32030
MathSciNet: MR3542776
Digital Object Identifier: 10.1215/21562261-3600184

Primary: 11F20 , 32S05 , 32S25 , 52B20

Keywords: Ehrhart polynomial , invariants of curve singularities , quotient surface singularity , rational polytope

Rights: Copyright © 2016 Kyoto University

Vol.56 • No. 3 • September 2016
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