Affiliation:
1. School of Mathematical Sciences , Peking University , Beijing 100871 , China
2. Department of Mathematics , Rutgers University , Piscataway, NJ 08857, USA
Abstract
Abstract
Let 𝒯
s,p,n
be the canonical blow-up of the Grassmann manifold G(p, n) constructed by blowing up the Plücker coordinate subspaces associated with the parameter s. We prove that the higher cohomology groups of the tangent bundle of 𝒯
s,p,n
vanish. As an application, 𝒯
s,p,n
is locally rigid in the sense of Kodaira-Spencer.
Reference13 articles.
1. [1] Bien, F. and Brion, M., Automorphisms and local rigidity of regular varieties, Compositio Math. 104 (1996), no. 1, 1-26.
2. [2] Białynicki-Birula, A., Some theorems on actions of algebraic groups, Ann. of Math. (2), 98, 1973.
3. [3] Bott, R., Homogeneous vector bundles, Ann. Math. 66 (1957) 203-248.
4. [4] Brion, M. and Pauer, F., Valuations des espaces homogènes sphériques, Comment. Math. Helv. 62 (1987), no. 2, 265–285.
5. [5] Brion, M., Spherical varieties: an introduction, Topological methods in algebraic transformation groups (New Brunswick, NJ, 1988), 11-26, Progr. Math., 80, Birkhäuser Boston, Boston, MA, 1989.