Let p:A \to Q be a double cover of a smooth quadric hypersurface Q^n \subset P^{n+1} branched alomg a smooth hypersurface. The paper deals with the problem of classisying pairs (X,L) where X is a smooth complex projective (n+1)-fold and L \in Pic(X) is either a very ample or an ample line bundle, whose complete linear system |L| contains a smooth element A as above. Complete answers are given for n \geq 3.
Double covers of smooth hyperquadrics as ample and very ample divisors / A. Lanteri. - In: ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG. - ISSN 0025-5858. - 64:1(1994), pp. 97-103.
Double covers of smooth hyperquadrics as ample and very ample divisors
A. LanteriPrimo
1994
Abstract
Let p:A \to Q be a double cover of a smooth quadric hypersurface Q^n \subset P^{n+1} branched alomg a smooth hypersurface. The paper deals with the problem of classisying pairs (X,L) where X is a smooth complex projective (n+1)-fold and L \in Pic(X) is either a very ample or an ample line bundle, whose complete linear system |L| contains a smooth element A as above. Complete answers are given for n \geq 3.
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