\begin{thebibliography}{IMOU16b}

\bibitem[Bea96]{Bea96}
Arnaud Beauville.
\newblock {\em Complex {A}lgebraic {S}urfaces}, volume~34 of {\em London
  Mathematical Society Student Texts}.
\newblock Cambridge University Press, Cambridge, second edition, 1996.
\newblock Translated from the 1978 French original by R. Barlow, with
  assistance from N. I. Shepherd-Barron and M. Reid.

\bibitem[Bor15]{Bor15}
Lev Borisov.
\newblock The class of the affine line is a zero divisor in the {G}rothendieck
  ring, 2015.
\newblock arXiv:1412.6194v3.

\bibitem[CG72]{CG72}
C.~Herbert Clemens and Phillip~A. Griffiths.
\newblock The intermediate {J}acobian of the cubic threefold.
\newblock {\em Ann. of Math. (2)}, 95:281--356, 1972.

\bibitem[CK89]{CK89}
Bruce Crauder and Sheldon Katz.
\newblock Cremona transformations with smooth irreducible fundamental locus.
\newblock {\em Amer. J. Math.}, 111(2):289--307, 1989.

\bibitem[DGPS15]{DGPS}
Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Sch\"onemann.
\newblock {\sc Singular} {4-0-2} --- {A} computer algebra system for polynomial
  computations.
\newblock \url{http://www.singular.uni-kl.de}, 2015.

\bibitem[Dol12]{Dol12}
Igor~V. Dolgachev.
\newblock {\em Classical Algebraic Geometry: A Modern View}.
\newblock Cambridge University Press, Cambridge, 2012.

\bibitem[Ful98]{Ful98}
William Fulton.
\newblock {\em Intersection theory}, volume~2 of {\em Ergebnisse der Mathematik
  und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics}.
\newblock Springer-Verlag, Berlin, 2nd edition, 1998.

\bibitem[GS14]{GS14}
Sergey Galkin and Evgeny Shinder.
\newblock The {F}ano variety of lines and rationality problem for a cubic
  hypersurface, 2014.
\newblock arXiv:1405.5154v2.

\bibitem[Has16]{Has16}
Brendan Hassett.
\newblock Cubic fourfolds, {K}3 surfaces, and rationality questions.
\newblock In {\em Rationality Problems in Algebraic Geometry}, volume 2172 of
  {\em Lecture Notes in Mathematics}. Springer, Cham; Fondazione C.I.M.E.,
  Florence, 2016.

\bibitem[HLOY03]{HLOY03}
Shinobu Hosono, Bong~H. Lian, Keiji Oguiso, and Shing-Tung Yau.
\newblock Fourier-{M}ukai partners of a {K}3 surface of {P}icard number one.
\newblock In {\em Vector bundles and representation theory ({C}olumbia, {MO},
  2002)}, volume 322 of {\em Contemp. Math.}, pages 43--55. Amer. Math. Soc.,
  Providence, RI, 2003.

\bibitem[IM04]{IM04}
Atanas Iliev and Dimitri Markushevich.
\newblock Elliptic curves and rank-2 vector bundles on the prime {F}ano
  threefold of genus 7.
\newblock {\em Adv. Geom.}, 4(3):287--318, 2004.

\bibitem[IMOU16a]{IMOU16G2}
Atsushi Ito, Makoto Miura, Shinnosuke Okawa, and Kazushi Ueda.
\newblock The class of the affine line is a zero divisor in the {G}rothendieck
  ring: via {$G_2$}-{G}rassmannians, 2016.
\newblock arXiv:1606.04210v2.

\bibitem[IMOU16b]{IMOU16K3}
Atsushi Ito, Makoto Miura, Shinnosuke Okawa, and Kazushi Ueda.
\newblock The class of the affine line is a zero divisor in the {G}rothendieck
  ring: via {K}3 surfaces of degree 12, 2016.
\newblock arXiv:1612.08497v1.

\bibitem[KS16]{KS16}
Alexander Kuznetsov and Evgeny Shinder.
\newblock Grothendieck ring of varieties, {D}- and {L}-equivalence, and
  families of quadrics, 2016.
\newblock arXiv:1612.07193v1.

\bibitem[Kuz06]{Kuz06}
A.~G. Kuznetsov.
\newblock Hyperplane sections and derived categories.
\newblock {\em Izv. Math.}, 70(3):447--547, 2006.

\bibitem[Kuz16]{Kuz16}
Alexander Kuznetsov.
\newblock Derived equivalence of {I}to-{M}iura-{O}kawa-{U}eda {C}alabi-{Y}au
  3-folds, 2016.
\newblock arXiv:1611.08386v1.

\bibitem[LL03]{LL03}
Michael Larsen and Valery~A. Lunts.
\newblock Motivic measures and stable birational geometry.
\newblock {\em Mosc. Math. J.}, 3(1):85--95, 259, 2003.

\bibitem[Mar11]{Mar11}
Eyal Markman.
\newblock A survey of {T}orelli and monodromy results for
  holomorphic-symplectic varieties.
\newblock In {\em Complex and differential geometry}, volume~8 of {\em Springer
  Proc. Math.}, pages 257--322. Springer, Heidelberg, 2011.

\bibitem[Muk87]{Muk87}
S.~Mukai.
\newblock On the moduli space of bundles on {$K3$} surfaces. {I}.
\newblock In {\em Vector bundles on algebraic varieties ({B}ombay, 1984)},
  volume~11 of {\em Tata Inst. Fund. Res. Stud. Math.}, pages 341--413. Tata
  Inst. Fund. Res., Bombay, 1987.

\bibitem[Muk88]{Muk88}
Shigeru Mukai.
\newblock Curves, {$K3$} surfaces and {F}ano {$3$}-folds of genus {$\leq10$}.
\newblock In {\em Algebraic geometry and commutative algebra, {V}ol.\ {I}},
  pages 357--377. Kinokuniya, Tokyo, 1988.

\bibitem[Muk99]{Muk99}
Shigeru Mukai.
\newblock Duality of polarized {$K3$} surfaces.
\newblock In {\em New trends in algebraic geometry ({W}arwick, 1996)}, volume
  264 of {\em London Math. Soc. Lecture Note Ser.}, pages 311--326. Cambridge
  Univ. Press, Cambridge, 1999.

\bibitem[Ogu02]{Ogu02}
Keiji Oguiso.
\newblock K3 surfaces via almost-primes.
\newblock {\em Math. Res. Lett.}, 9(1):47--63, 2002.

\bibitem[Orl97]{Orl97}
D.~O. Orlov.
\newblock Equivalences of derived categories and {$K3$} surfaces.
\newblock {\em J. Math. Sci. (New York)}, 84(5):1361--1381, 1997.
\newblock Algebraic geometry, 7.

\bibitem[Som81]{Som81}
Andrew~John Sommese.
\newblock Hyperplane sections.
\newblock In {\em Algebraic geometry ({C}hicago, {I}ll., 1980)}, volume 862 of
  {\em Lecture Notes in Math.}, pages 232--271. Springer, Berlin-New York,
  1981.

\end{thebibliography}