On the generalization of Kummer surfaces
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.
resolving singularities of the quotient of a complex torus by a finite abelian group
scientific article; zbMATH DE number 4079612
scientific article