Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Varieties of minimal rational tangents on double covers of projective
  space   Let $\phi: X \to \mathbb P^n$ be a double cover branched along a smooth
hypersurface of degree $2m, 2 \leq m \leq n-1$. We study the varieties of
minimal rational tangents $\mathcal C_x \subset \mathbb P T_x(X)$ at a general
point $x$ of $X$. We describe the homogeneous ideal of $\mathcal C_x$ and show
that the projective isomorphism type of $\mathcal C_x$ varies in a maximal way
as $x$ varies over general points of $X$. Our description of the ideal of
$\mathbb C_x$ implies a certain rigidity property of the covering morphism
$\phi$. As an application of this rigidity, we show that any finite morphism
between such double covers with $m=n-1$ must be an isomorphism. We also prove
that Liouville-type extension property holds with respect to minimal rational
curves on $X$.

35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics