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

Narasimha Chary Bonala (1)

1 IF - Institut Fourier

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 be the Bott–Samelson–Demazure–Hansen (BSDH) variety corresponding to a reduced expression of w with respect to the data In this article we give complete characterization of the expressions such that the corresponding BSDH variety 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.

Domaines: Mathématiques [math]

Narasimha Chary Bonala. On Fano and weak Fano Bott–Samelson–Demazure–Hansen varieties. Journal of Pure and Applied Algebra, 2018, 222 (9), pp.2552 - 2561. ⟨10.1016/j.jpaa.2017.10.006⟩. ⟨hal-01869500⟩