Abstract
AbstractLet 𝒯s,p,nbe the canonical blow-up of the Grassmann manifoldG(p,n) constructed by blowing up the Plücker coordinate subspaces associated with the parameters. We prove that the higher cohomology groups of the tangent bundle of 𝒯s,p,nvanish. As an application, 𝒯s,p,nis locally rigid in the sense of Kodaira-Spencer.
Highlights
We prove that the higher cohomology groups of the tangent bundle of Ts,p,n vanish
Sheaf cohomology of vector bundles is a fundamental object studied in complex geometry and algebraic geometry
KodairaSpencer theory relates the local deformation of the complex structure of a complex manifold X to the rst cohomology of its tangent bundle H (X, TX)
Summary
Sheaf cohomology of vector bundles is a fundamental object studied in complex geometry and algebraic geometry. Computation yields that in our case the restriction of the anticanonical bundle of Ts,p,n to the components of the boundary divisors is big and numerical e ective, which is su cient to apply the Kawamata-Viehweg vanishing theorem. Let D be an irreducible divisor of D−j
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