Grothendieck ring of varieties, D and Lequivalence, and families of quadrics
Abstract
We discuss a conjecture saying that derived equivalence of simply connected smooth projective 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 ${\mathbf P}^5$ and the corresponding double cover $Y \to {\mathbf P}^2$ 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.07193
 Bibcode:
 2016arXiv161207193K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology
 EPrint:
 Exposition improved, main conjecture slightly updated