Kyoto Journal of Mathematics

Numerical adjunction formulas for weighted projective planes and lattice point counting

José Ignacio Cogolludo-Agustín, Jorge Martín-Morales, and Jorge Ortigas-Galindo

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Abstract

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.

Article information

Source
Kyoto J. Math., Volume 56, Number 3 (2016), 575-598.

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1471872282

Digital Object Identifier
doi:10.1215/21562261-3600184

Mathematical Reviews number (MathSciNet)
MR3542776

Zentralblatt MATH identifier
1353.32030

Subjects
Primary: 32S05: Local singularities [See also 14J17] 32S25: Surface and hypersurface singularities [See also 14J17] 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 11F20: Dedekind eta function, Dedekind sums

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

Citation

Cogolludo-Agustín, José Ignacio; Martín-Morales, Jorge; Ortigas-Galindo, Jorge. Numerical adjunction formulas for weighted projective planes and lattice point counting. Kyoto J. Math. 56 (2016), no. 3, 575--598. doi:10.1215/21562261-3600184. https://projecteuclid.org/euclid.kjm/1471872282


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