Subvarieties of generic hypersurfaces in any variety

Details Subvarieties of generic hypersurfaces in any variety Subvarieties of generic hypersurfaces in any variety

1999-01-20

arxiv.org/abs/math/9901083v2

Mathematics

Algebraic Geometry

We made some improvements in the introduction and definitions. In an effort to clarify the arguments we separated the 1-fillin

Scientific paper

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a smooth m-fold Y. We suppose that f is r-filling, i.e. upon deforming X in $H^0(L^d)$, f deforms in a family such that the corresponding deformations of $Y^r$ dominate $W^r$. Under these hypotheses we give a lower bound for the dimension of a certain linear system on the Cartesian product $Y^r$ having certain vanishing order on a diagonal locus as well as on a double point locus. This yields as one application a lower bound on the dimension of the linear system |K_{Y} - (d - n + m)f^*L - f^*K_{W}| which generalizes results of Ein and Xu (and in weaker form, Voisin). As another perhaps more surprising application, we conclude a lower bound on the number of quadrics containing certain projective images of Y.

Affiliated with

Also associated with

No associations

Rating

Subvarieties of generic hypersurfaces in any variety does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Subvarieties of generic hypersurfaces in any variety, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Subvarieties of generic hypersurfaces in any variety will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-6140