Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log-terminal singularities and vanishing theorems   Generalizing work of Smith and Hara, we give a new characterization of
log-terminal singularities for finitely generated algebras over $\mathbb C$, in
terms of purity properties of ultraproducts of characteristic $p$ Frobenii.
  The first application is a Bout\^ot-type theorem for log-terminal
singularities: given a pure morphism $Y\to X$ between affine $\mathbb
Q$-Gorenstein varieties of finite type over $\mathbb C$, if $Y$ has at most a
log-terminal singularities, then so does $X$. The second application is the
Vanishing for Maps of Tor for log-terminal singularities: if $A\subset R$ is a
Noether Normalization of a finitely generated $\mathbb C$-algebra $R$ and $S$
is a finitely generated $R$-algebra with log-terminal singularities, then the
natural morphism $\operatorname{Tor}^A_i(M,R) \to \operatorname{Tor}^A_i(M,S)$
is zero, for every $A$-module $M$ and every $i\geq 1$. The final application is
the Kawamata-Viehweg Vanishing Theorem for a connected projective variety $X$
of finite type over $\mathbb C$ whose affine cone has a log-terminal vertex
(for some choice of polarization). As a smooth Fano variety has this latter
property, we obtain a proof of the following conjecture of Smith for quotients
of smooth Fano varieties: if $G$ is the complexification of a real Lie group
acting algebraically on a projective smooth Fano variety $X$, then for any
numerically effective line bundle $\mathcal L$ on any GIT quotient $Y:=X//G$,
each cohomology module $H^i(Y,\mathcal L)$ vanishes for $i>0$, and, if
$\mathcal L$ is moreover big, then $H^i(Y,\mathcal L^{-1})$ vanishes for
$i<\operatorname{dim}Y$.

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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph