Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Th\'eor\`emes De Connexit\'e Pour Les Produits D'Espaces Projectifs et
  Les Grassmanniennes   Let $G$ be the Grassmannian $G(d,n)$, let $X$ and $Y$ be complete irreducible
varieties, and let $X\rightarrow G$ and $Y\rightarrow G$ be morphisms. Hansen
proved that $X \times_G Y$ is connected when $codim f(X) + codim g(Y) < n$. We
show that the conclusion holds under the often weaker hypothesis
$f(X).g(Y).T\ne 0$, where $T$ is the class of $G(d,n-1)$ in $G$.
  We prove similar results when $G$ is a product of projective spaces. In
particular, if $D$ is an irreducible subvariety of $P^n\times P^n$ of dimension
$n$ which dominates both factors, and if $X$ is complete irreducible, with a
morphism $f: X \rightarrow P^n\times P^n$ such that $dim f(X) >n$, $f^{-1}(D)$
is connected. This extends the classical Fulton-Hansen connectedness theorem.
These results illustrate Fulton and Lazarsfeld's idea that connectedness should
be a numerical property.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin