Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subvarieties of generic hypersurfaces in any variety   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.

19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg