Wirtinger numbers and holomorphic symplectic immersions

• Misha Verbitsky ^[1]
  1. [1] University of Glasgow

     University of Glasgow

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 4, 2005, págs. 551-559
• Idioma: inglés
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• Resumen

  • For any subvariety of a compact holomorphic symplectic Kähler manifold, we define the symplectic Wirtinger number W(X). We show that W(X)⩽1, and the equality is reached if and only if the subvariety X⊂M is trianalytic, i.e. compatible with the hyperkähler structure on M. For a sequence X1→X2→…Xn→M of immersions of simple holomorphic symplectic manifolds, we show that W(X1)⩽W(X2)⩽…⩽W(Xn).