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<p>Let <i>G</i> be a connected simply connected semisimple complex algebraic group and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P\, \subset \, G\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mspace width="0.166667em" /> <mo>⊂</mo> <mspace width="0.166667em" /> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation> a parabolic subgroup. We give a necessary and sufficient condition for a line bundle — on the blow-up of the generalized flag variety <i>G</i>/<i>P</i> along a smooth Schubert variety — to be ample (respectively, nef). Furthermore, it is shown that every such nef line bundle is actually globally generated. As a consequence, we are able to describe when such a blow-up is (weak) Fano.</p>

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Blow-up of a Generalized Flag Variety

  • 期刊论文

  • 发表日期：

    2025年10月4日

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  • Indranil Biswas,
  • Pinakinath Saha

摘要

Let G be a connected simply connected semisimple complex algebraic group and \(P\, \subset \, G\) P ⊂ G a parabolic subgroup. We give a necessary and sufficient condition for a line bundle — on the blow-up of the generalized flag variety G/P along a smooth Schubert variety — to be ample (respectively, nef). Furthermore, it is shown that every such nef line bundle is actually globally generated. As a consequence, we are able to describe when such a blow-up is (weak) Fano.