A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic
symplectic forms such that any linear combination of these forms has constant
rank 2n, n or 0, and degenerate forms in Ω belong to a non-degenerate
quadric hypersurface. We show that a trisymplectic manifold is equipped with a
holomorphic 3-web and the Chern connection of this 3-web is holomorphic,
torsion-free, and preserves the three symplectic forms. We construct a
trisymplectic structure on the moduli of regular rational curves in the twistor
space of a hyperkaehler manifold, and define a trisymplectic reduction of a
trisymplectic manifold, which is a complexified form of a hyperkaehler
reduction. We prove that the trisymplectic reduction in the space of regular
rational curves on the twistor space of a hyperkaehler manifold M is compatible
with the hyperkaehler reduction on M.
As an application of these geometric ideas, we consider the ADHM construction
of instantons and show that the moduli space of rank r, charge c framed
instanton bundles on CP^3 is a smooth, connected, trisymplectic manifold of
complex dimension 4rc. In particular, it follows that the moduli space of rank
2, charge c instanton bundles on CP^3 is a smooth complex manifold dimension
8c-3, thus settling a 30-year old conjecture.Comment: 42 pages, v. 3.2, changes in section 3.1: the notion of trisymplectic
structure stated differently, Clifford algebra action introduce
