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

@article{Kuznetsov2018GrothendieckRO, title={Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics}, author={Alexander Kuznetsov and Evgeny Shinder}, journal={Selecta Mathematica}, year={2018}, volume={24}, pages={3475-3500} }

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 $${\mathbb {P}}^5$$P5 and the corresponding double cover $$Y \rightarrow {\mathbb {P}}^2$$Y→P2 branched over a… CONTINUE READING

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