Wirtinger numbers and holomorphic symplectic immersions

Details Wirtinger numbers and holomorphic symplectic immersions Wirtinger numbers and holomorphic symplectic immersions

1998-12-14

arxiv.org/abs/math/9812077v3

Selecta Math. (N.S.) 10 (2004), no. 4, 551--559.

Mathematics

Algebraic Geometry

minor corrections - September 1999; 10 pages

Scientific paper

For any subvariety of a compact holomorphic symplectic Kaehler manifold, we define the number W(X), which we call Wirtinger number. We show that $W(X)\leq 1$, and the equality is reached if and only if the subvariety $X\subset M$ is trianalytic, i. e. compactible with the hyperkaehler structure on M. For a sequence $X_1 \arrow X_2 \arrow ... X_n\arrow M$ of immersions of simple holomorphic symplectic manifolds, we show that $W(X_1) \leq W(X_2) \leq >... \leq W(X_n)$.

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