Wirtinger numbers and holomorphic symplectic immersions |
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Authors: | Misha Verbitsky |
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Institution: | (1) Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK |
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Abstract: | For any subvariety of a compact holomorphic symplectic Kähler manifold, we define the symplectic Wirtinger number W(X). We show that
and the equality is reached if and only if the subvariety
is trianalytic, i.e. compatible with the hyperkähler structure on M. For a sequence
of immersions of simple holomorphic symplectic manifolds, we show that
![$W\left( {X_1 } \right) \leqslant W\left( {X_2 } \right) \leqslant \ldots \leqslant W\left( {X_n } \right).$](/content/n2n73101014r441h/29_2004_Article_0268_TeX2GIFIEq4.gif) |
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Keywords: | 53C26 |
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