Some algebraic and geometric properties of hyper-K\"ahler fourfold symmetries
Abstract
We complete the classification of order 5 nonsymplectic automorphisms on hyper-K\"ahler fourfolds deformation equivalent to the Hilbert square of a K3 surface. We then compute the topological Lefschetz number of natural automorphisms of generalized Kummer fourfolds and we describe the geometry of their fix loci.
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