Period Maps and Cohomology Cohomology of Compact Hyperkähler Manifolds
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چکیده
Let M be a compact simply connected hy-perkähler (or holomorphically symplectic) manifold, dim H 2 (M) = n. Assume that M is not a product of hyperkaehler manifolds. We prove that the Lie group 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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تاریخ انتشار 1995