A note on toric degeneration of a Bott-Samelson-Demazure-Hansen variety

Narasimha Chary Bonala (1)

1 IF - Institut Fourier

In this paper we study the geometry of toric degeneration of a Bott-Samelson-Demazure-Hansen (BSDH) variety. We give some applications to BSDH varieties. Precisely, we classify Fano, weak Fano and log Fano BSDH varieties and their toric limits in Kac-Moody setting. We prove some vanishing theorems for the cohomology of tangent bundle (and line bundles) on BSDH varieties. We also recover the results in arxiv.org/abs/1604.01998, by toric methods.

Mots clés: Bott-Samelson-Demazure-Hansen varieties; canonical line bundle; tangent bundle and toric varieties

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Narasimha Chary Bonala. A note on toric degeneration of a Bott-Samelson-Demazure-Hansen variety. 2017. ⟨hal-01617037⟩