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Non-trivial smooth families of K3 surfaces

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Abstract

Let X be a complex K3 surface, \(\textrm{Diff}(X)\) the group of diffeomorphisms of X and \(\textrm{Diff}_0(X)\) the identity component. We prove that the fundamental group of \(\textrm{Diff}_0(X)\) contains a free abelian group of countably infinite rank as a direct summand. The summand is detected using families Seiberg–Witten invariants. The moduli space of Einstein metrics on X is used as a key ingredient in the proof.

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  1. School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, 5005, Australia

    David Baraglia

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  1. David Baraglia
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Baraglia, D. Non-trivial smooth families of K3 surfaces. Math. Ann. 387, 1719–1744 (2023). https://doi.org/10.1007/s00208-022-02508-3

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