Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Fano and weak Fano Bott-Samelson-Demazure-Hansen varieties   Let $G$ be a simple algebraic group over the field of complex numbers. Fix a
maximal torus $T$ and a Borel subgroup $B$ of $G$ containing $T$. Let $w$ be an
element of the Weyl group $W$ of $G$, and let $Z(\tilde w)$ be the
Bott-Samelson-Demazure-Hansen (BSDH) variety corresponding to a reduced
expression $\tilde w$ of $w$ with respect to the data $(G, B, T)$. In this
article we give complete characterization of the expressions $\tilde w$ such
that the corresponding BSDH variety $Z(\tilde w)$ is Fano or weak Fano. As a
consequence we prove vanishing theorems of the cohomology of tangent bundle of
certain BSDH varieties and hence we get some local rigidity results.

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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin