Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics

• Alexander Kuznetsov ^[2] ; Evgeny Shinder ^[1]
  1. [1] University of Sheffield

     University of Sheffield

     Reino Unido

     
  2. [2] University of Moscow, Rusia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3475-3500
• Idioma: inglés
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• Resumen

  • We discuss a conjecture saying that derived equivalence of smooth projective simply connected varieties implies that the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line class. We support the conjecture with a number of known examples, and one new example. We consider a smooth complete intersection X of three quadrics in P5 and the corresponding double cover Y → P2 branched over a sextic curve. We show that as soon as the natural Brauer class on Y vanishes, so that X and Y are derived equivalent, the difference [X]−[Y ] is annihilated by the affine line class.