Mathematics Seminar
Date: Wednesday, 3 April 2024
Time: 3:40 to 4:30 PM
Venue: Lecture Hall 202
Some recent results related to Bott-Samelson-Demazure-Hansen varieties.
Senthamarai Kannan
Chennai Mathematical Institute.
03-04-24

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Abstract

Let $G$ be a semisimple algebraic group over $\mathbb{C}$, $T$ a maximal torus of $G$ and $B$ a Borel subgroup of $G$ containing $T$.

Let $W=N_G(T)/T$ be the Weyl group of $G$ relative to $T$. Let $G/B$ be the full flag variety of all Borel subgroups of $G$. For $w\in W$, let $X(w)=\overline{BwB/B}$ be the Schubert variety corresponding to $w$. Schubert varieties are normal but there are Schubert varieties that are not smooth. Bott and Samelson constructed desingularisation $Z(w, \underline{i})$ of $X(w)$ corresponding to every reduced expression $\underline{i}$ of $w$, in a differential geometric context. Demazure and Hansen constructed these desingularisations using algebraic geometric method. So, these varieties are known as Bott-Samelson-Demazure-Hansen varieties.