# 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}
}
• Published 2018
• Mathematics
• Selecta Mathematica
• 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

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 15 CITATIONS

## Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

• Mathematics
• 2016

## Intersections of two Grassmannians in $\mathbf{P}^9$

• Mathematics
• 2017
VIEW 2 EXCERPTS
CITES BACKGROUND

## Intersections of two Grassmannians in ℙ9

• Mathematics
• 2018
VIEW 2 EXCERPTS
CITES BACKGROUND

## Some remarks on L-equivalence of algebraic varieties

VIEW 1 EXCERPT
CITES BACKGROUND
HIGHLY INFLUENCED

## L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces

• Mathematics
• 2020

## Cremona transformations and derived equivalences of K3 surfaces

• Mathematics
• 2016

## Symmetric locally free resolutions and rationality problem of quadric bundles

• Mathematics
• 2020

## Gushel--Mukai varieties: intermediate Jacobians

• Mathematics
• 2020

## Motives of isogenous K3 surfaces

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 30 REFERENCES

## Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

• Mathematics
• 2016

## The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians

• Mathematics
• 2016

## Derived categories of torsors for abelian schemes

• Mathematics
• 2014

## Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems

• Mathematics
• 2014

## The Grothendieck ring of varieties and piecewise isomorphisms

• Mathematics
• 2010

## The class of the affine line is a zero divisor in the Grothendieck ring: via K3 surfaces of degree 12

• Mathematics
• 2016

## The Fano variety of lines and rationality problem for a cubic hypersurface

• Mathematics
• 2014