On the generalization of Kummer surfaces
type: Item
instance of: scholarly article
title: On the generalization of Kummer surfaces
zbMATH Open document ID: 0661.14031
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: In this paper, we study the following problem: ``Find the projective manifolds V/G with trivial canonical bundle and zero first Betti number by the construction of resolving singularities of the quotient of a complex torus V by a finite abelian group G. Computer their Euler numbers.'' By the toroidal desingularization, we find a criterion for the existence of such V/G for those (V,G) with trivial dualizing sheaf \(\omega_{V/G}\). Because the dimension of V is 2 or 3, such V/G can always be constructed. We also derive a formula of the Euler number of V/G in terms of the Euler numbers of fixed points of elements of G, which was suggested by string theorists.
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14F45
zbMATH DE Number: 4079612
zbMATH Keywords: Kummer surfaces
zbMATH Keywords: resolving singularities of the quotient of a complex torus by a finite abelian group
zbMATH Keywords: Euler numbers
zbMATH Keywords: toroidal desingularization
zbMATH Keywords: string
author: Shi-Shyr Roan
reviewed by: Shi-Shyr Roan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214443600
OpenAlex ID: W1555620679
Wikidata QID: Q115182521
DOI: 10.4310/JDG/1214443600
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description: scientific article; zbMATH DE number 4079612