Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic
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Original versionHonigs, Lombardi L, Tirabassi S. Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic. Mathematische Zeitschrift. 2019 https://doi.org/10.1007/s00209-019-02362-1
We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable sheaves. We apply this fact to show that the set of Fourier–Mukai partners of a canonical cover of a hyperelliptic or Enriques surface over an algebraically closed field of characteristic greater than three is trivial. These results extend earlier results of Bridgeland–Maciocia and Sosna to positive characteristic.