Geodesic
On Topological Properties of Some Coverings. An Addendum to a Paper of Lanteri and Struppa
Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 206-214

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Wiśniewski, Jarosław A. On Topological Properties of Some Coverings. An Addendum to a Paper of Lanteri and Struppa. Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 206-214. doi: 10.4153/CJM-1992-013-8
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