Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T15:55:03.406Z Has data issue: false hasContentIssue false
  • English
  • Français

On Topological Properties of Some Coverings. An Addendum to a Paper of Lanteri and Struppa

Published online by Cambridge University Press:  20 November 2018

Jarosław A. Wiśniewski
Jarosław A. Wiśniewski*
Affiliation:
Warsaw University, Institute of Mathematics, ul. Banacha 2, 00-913 Warszawa, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let π: X′ → X be a finite surjective morphism of complex projective manifolds which can be factored by an embedding of X′ into the total space of an ample line bundle 𝓛 over X. A theorem of Lazarsfeld asserts that Betti numbers of X and X′ are equal except, possibly, the middle ones. In the present paper it is proved that the middle numbers are actually non-equal if either 𝓛 is spanned and deg π ≥ dim X, or if X is either a hyperquadric or a projective space and π is not a double cover of an odd-dimensional projective space by a hyperquadric.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 206 - 214
Copyright
Copyright © Canadian Mathematical Society 1989

References

[Fu] Fujita, T., Triple covers by smooth manifolds, J. Fac. Sci. Univ. Tokyo 35(1988), 169–175.Google Scholar
[GH] Griffiths, Ph. and Harris, J., Principles of algebraic geometry. John Wiley & Sons, 1978.Google Scholar
[Ha] Hartshorne, R., Algebraic'geometry. Springer-Verlag, 1977.Google Scholar
[Hi] Hirzebruch, F., Topological methods in algebraic geometry. Springer-Verlag, 1978.Google Scholar
[LP] Lanteri, A. and M. Palletschi, About the adjunction process for polarized algebraic surfaces, J. reine angew. Math. 352(1984), 15–23.Google Scholar
[LS] Lanteri, A. and Struppa, D., On topological properties of cyclic coverings branched along an ample divisor, Can. J. Math. 41(1989), 462–479.Google Scholar
[La] Lazarsfeld, R., A Barth-type theorem for branched coverings of projective space, Math. Ann. 249(1980), 163–176.Google Scholar
[Sn] Snow, D.M., Cohomology of twisted holomorphic forms on Grassmann manifolds andquadric hypersurfaces, Math. Ann. 276(1986), 159–176.Google Scholar
[So] Sommese, A. J., On adjunction theoretic structure of projective varieties, in Complex analysis and algebraic geometry, 175–213. Lecture Notes Math. 1194, Springer-Verlag, 1986.Google Scholar