Cohomology of compact hyperkaehler manifolds

Details Cohomology of compact hyperkaehler manifolds Cohomology of compact hyperkaehler manifolds

1995-01-03

arxiv.org/abs/alg-geom/9501001v2

Mathematics

Algebraic Geometry

87 pages LaTeX 2.09

Scientific paper

Let M be a compact simply connected hyperk\"ahler (or holomorphically symplectic) manifold, \dim H^2(M)=n. Assume that M is not a product of hyperkaehler manifolds. We prove that the Lie algebra so(n-3,3) acts by automorphisms on the cohomology ring H^*(M). Under this action, the space H^2(M) is isomorphic to the fundamental representation of so(n-3,3). Let A^r be the subring of H^*(M) generated by H^2(M). We construct an action of the Lie algebra so(n-2,4) on the space A, which preserves A^r. The space A^r is an irreducible representation of so(n-2,4). This makes it possible to compute the ring A^r explicitely.

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