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Birational geometry of compactifications of Drinfeld half-spaces over a finite field. (arXiv:1711.05281v1 [math.AG])
来源于:arXiv
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. 查看全文>>