CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Restriction of the Tangent Bundle of $G/P$ to a Hypersurface

  Published:2009-12-04
 Printed: Jun 2010
  • Indranil Biswas
Format:   HTML   LaTeX   MathJax  

Abstract

Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable.
Keywords: tangent bundle, homogeneous space, semistability, hypersurface tangent bundle, homogeneous space, semistability, hypersurface
MSC Classifications: 14F05, 14J60, 14M15 show english descriptions Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/