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)

Read more

Summary

Introduction

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

Results
Conclusion
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.