Subvarieties of generic hypersurfaces in any variety
| dc.creator | Chiantini, L. | |
| dc.creator | Lopez, A. F. | |
| dc.creator | Ran, Z. | |
| dc.date | 1999-01-20 | |
| dc.date | 2001-02-09 | |
| dc.date.accessioned | 2026-07-07T05:27:36Z | |
| dc.date.available | 2026-07-07T05:27:36Z | |
| dc.description | 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. | |
| dc.description | We made some improvements in the introduction and definitions. In an effort to clarify the arguments we separated the 1-filling case from the r-filling case and we gave a more detailed proof of the key lemma. The article will appear in the Math. Proc. Cambridge Philos. Soc | |
| dc.identifier | https://arxiv.org/abs/math/9901083 | |
| dc.identifier | http://arxiv.org/abs/math/9901083 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77976 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C99; 14J70 | |
| dc.title | Subvarieties of generic hypersurfaces in any variety | |
| dc.type | text |