On involutions with middle-dimensional fixed-point locus and holomorphic-symplectic manifolds |
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Authors: | George Thompson |
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Institution: | 1. ICTP, P.O. Box 586, 34100?, Trieste, Italy
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Abstract: | Let $g$ be an involution of a compact closed manifold $X$ such that the fixed-point set $X^{g}$ is middle dimensional. Under the assumption that the normal bundle of the fixed-point set is either the tangent or co-tangent bundle conditions on the equivariant invariants of $X$ arise. In particular if $X$ is a holomorphic-symplectic manifold and $g$ an anti holomorphic-symplectic involution one arrives at a generalisation of Beauville’s result that for $X$ a hyper-Kähler manifold the $\hat{A}$ genus of $X^{g}$ is one. |
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