Weighted complete intersections and lattice points
type: Item
instance of: scholarly article
title: Weighted complete intersections and lattice points
zbMATH Open document ID: 0815.14030
DOI: 10.1007/BF02571899
author: Robert Laterveer
published in: Mathematische Zeitschrift
publication date: 1995-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/174724
review text: Let \(S\) be a quasismooth weighted complete intersection surface of multidegree \((d_ 1, \dots, d_{n-2})\) in a weighted projective space \(\mathbb{P} (q_ 0, \dots, q_ n)\), such that \(\text{lcm} \{q_ i\}\) divides all \(d_ j\). Using two results which \textit{F. Hirzebruch} and \textit{P. Zagier} established as corollaries of the Atiyah-Singer theorem [cf. ``The Atiyah-Singer theorem and elementary number theory'' (1974; Zbl 0288.10001)], an explicit expression for the geometric genus of \(S\) is given. By an elementary observation, this expression implies the Mordell-Pommersheim formula on the number of lattice points in the tetrahedron in \(\mathbb{Z}^ 3\) with vertices (0,0,0), \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\).
Mathematics Subject Classification ID: 14J99
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 737182
zbMATH Keywords: weighted complete intersection surface
zbMATH Keywords: geometric genus
zbMATH Keywords: number of lattice points
MaRDI profile type: Publication
cites work: Q5749404
cites work: Picard numbers of surfaces in 3-dimensional weighted projective spaces
cites work: Espaces projectifs anisotropes
cites work: Generic Torelli for weighted hypersurfaces
cites work: Q5328234
cites work: Q4775913
cites work: Toric varieties, lattice points and Dedekind sums
description: scientific article; zbMATH DE number 737182