Nef divisors for moduli spaces of complexes with compact support

• Arend Bayer ^[1] ; Alastair Craw ^[2] ; Ziyu Zhang ^[3]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] University of Bath

     University of Bath

     Reino Unido

     
  3. [3] University of Hannover

     University of Hannover

     Region Hannover, Alemania

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1507-1561
• Idioma: inglés
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• Resumen

  • In Bayer and Macrì (J Am Math Soc 27(3):707–752, 2014), the first author and Macrì constructed a family of nef divisors on any moduli space of Bridgelandstable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated scheme Y of finite type over a field, where we consider moduli spaces of Bridgeland-stable objects on Y with compact support.

    We also show that the nef divisor is compatible with the polarising ample line bundle coming from the GIT construction of the moduli space in the special case when Y admits a tilting bundle and the stability condition arises from a θ-stability condition for the endomorphism algebra. Our main tool generalises the work of Abramovich– Polishchuk (J Reine Angew Math 590:89–130, 2006) and Polishchuk (Mosc Math J 7(1):109–134, 2007): given a t-structure on the derived category Dc(Y ) on Y of objects with compact support and a base scheme S, we construct a constant family of t-structures on a category of objects on Y × S with compact support relative to S.