Resumen de Wirtinger numbers and holomorphic symplectic immersions

Misha Verbitsky

• 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).