Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birational geometry of compactifications of Drinfeld half-spaces over a
  finite field   We study compactifications of Drinfeld half-spaces over a finite field. In
particular, we construct a purely inseparable endomorphism of Drinfeld's
half-space $\Omega (V)$ over a finite field $k$ that does not extend to an
endomorphism of the projective space $P (V)$. This should be compared with
theorem of R\'emy, Thuillier and Werner that every $k$-automorphism of $\Omega
(V)$ extends to a $k$-automorphism of $P (V)$. Our construction uses an
inseparable analogue of the Cremona transformation. We also study foliations on
Drinfeld's half-spaces. This leads to various examples of interesting varieties
in positive characteristic. In particular, we show a new example of a
non-liftable projective Calabi-Yau threefold in characteristic $2$ and we show
examples of rational surfaces with klt singularities, whose cotangent bundle
contains an ample line bundle.

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The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio