ArticleOriginal scientific text
Title
Hodge numbers of a double octic with non-isolated singularities
Authors 1
Affiliations
- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Abstract
If B is a surface in ℙ³ of degree 8 which is the union of two smooth surfaces intersecting transversally then the double covering of ℙ³ branched along B has a non-singular model which is a Calabi-Yau manifold. The aim of this note is to compute the Hodge numbers of this manifold.
Keywords
Hodge numbers, double solids, Calabi-Yau manifolds, surface singularities
Bibliography
- W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Springer, Berlin, 1984.
- C. H. Clemens, Double solids, Adv. Math. 47 (1983), 107-230.
- S. Cynk, Hodge numbers of nodal double octics, Comm. Algebra 27 (1999), 4097-4102.
- S. Cynk, Double octics with isolated singularities, Adv. Theor. Math. Phys. 3 (1999), 217-225.
- S. Cynk and T. Szemberg, Double covers and Calabi-Yau varieties, in: Banach Center Publ. 44, Inst. Math., Polish Acad. Sci., 1998, 93-101.
- A. Dimca, Betti numbers of hypersurfaces and defects of linear systems, Duke Math. J. 60 (1990), 285-298.
- R. Hartshorne, Algebraic Geometry, Springer, Heidelberg, 1977.