On Fano and weak Fano Bott-Samelson-Demazure-Hansen varieties

Abstract

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.

Accepted in Journal of Pure and Applied Algebra

References in corpus (2)

• Schubert varieties are log Fano over the integers
• A note on toric degeneration of a Bott-Samelson-Demazure-Hansen variety