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.
@article{bwmeta1.element.bwnjournal-article-apmv73z3p221bwm,
author = {Cynk, S\l awomir},
title = {Hodge numbers of a double octic with non-isolated singularities},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {221-226},
zbl = {0983.14016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p221bwm}
}
Cynk, Sławomir. Hodge numbers of a double octic with non-isolated singularities. Annales Polonici Mathematici, Tome 75 (2000) pp. 221-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p221bwm/
[000] [1] W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Springer, Berlin, 1984. | Zbl 0718.14023
[001] [2] C. H. Clemens, Double solids, Adv. Math. 47 (1983), 107-230. | Zbl 0509.14045
[002] [3] S. Cynk, Hodge numbers of nodal double octics, Comm. Algebra 27 (1999), 4097-4102. | Zbl 0958.14032
[003] [4] S. Cynk, Double octics with isolated singularities, Adv. Theor. Math. Phys. 3 (1999), 217-225. | Zbl 0964.14032
[004] [5] S. Cynk and T. Szemberg, Double covers and Calabi-Yau varieties, in: Banach Center Publ. 44, Inst. Math., Polish Acad. Sci., 1998, 93-101. | Zbl 0915.14025
[005] [6] A. Dimca, Betti numbers of hypersurfaces and defects of linear systems, Duke Math. J. 60 (1990), 285-298. | Zbl 0729.14017
[006] [7] R. Hartshorne, Algebraic Geometry, Springer, Heidelberg, 1977.