Tokyo Journal of Mathematics

On the Motive of Ito--Miura--Okawa--Ueda Calabi--Yau Threefolds

Robert LATERVEER

Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Ito, Miura, Okawa and Ueda have constructed a pair of Calabi--Yau threefolds $X$ and $Y$ that are L-equivalent and derived equivalent, but not stably birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.

Article information

Source
Tokyo J. Math., Advance publication (2019), 6 pages.

Dates
First available in Project Euclid: 24 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1566612093

Subjects
Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture

Citation

LATERVEER, Robert. On the Motive of Ito--Miura--Okawa--Ueda Calabi--Yau Threefolds. Tokyo J. Math., advance publication, 24 August 2019. https://projecteuclid.org/euclid.tjm/1566612093


Export citation

References

  • S. Bloch and V. Srinivas, Remarks on correspondences and algebraic cycles, American Journal of Mathematics Vol. 105, No. 5 (1983), 1235–1253.
  • L. Borisov, Class of the affine line is a zero divisor in the Grothendieck ring, Journal of Alg. Geom. 27, No. 2 (2018), 203–209.
  • H. Esnault, M. Levine and E. Viehweg, Chow groups of projective varieties of very small degree, Duke Math. Journal 87, No. 1 (1997), 29–58.
  • K. Honigs, Derived equivalence, Albanese varieties, and the zeta functions of $3$-dimensional varieties (with an appendix by J. Achter, S. Casalaina–Martin, K. Honigs and Ch. Vial), Proc. Amer. Math. Soc.
  • D. Huybrechts, Motives of derived equivalent $K3$ surfaces, Abhandlungen Math. Sem. Univ. Hamburg 88, No. 1 (2018), 201–207.
  • A Ito, M. Miura, S. Okawa and K. Ueda, The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians, arXiv:1606.04210.
  • A. Kuznetsov, Derived equivalence of Ito–Miura–Okawa–Ueda Calabi–Yau 3-folds, Journal of the Math. Soc. Japan 70, No. 3 (2018), 1007–1013.
  • A. Kuznetsov and E. Shinder, Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics, Selecta Math. 24, No. 4 (2018), 3475–3500.
  • J. Murre, J. Nagel and C. Peters, Lectures on the theory of pure motives, Amer. Math. Soc. University Lecture Series 61, Providence 2013.
  • D. Orlov, Derived categories of coherent sheaves and motives, Uspekhi Mat. Nauk, 60, No. 6 (2005), 231–232, translation in Russian Math. Surveys 60, No. 6 (2005), 1242–1244.
  • J. Ottem and J. Rennemo, A counterexample to the birational Torelli problem for Calabi–Yau threefolds, Journal of the London Math. Soc. 97 (2018), 427–440.
  • T. Scholl, Classical motives, in: Motives (U. Jannsen et alii, eds.), Proceedings of Symposia in Pure Mathematics Vol. 55 (1994), Part 1.
  • Ch. Vial, Algebraic cycles and fibrations, Documenta Math. 18 (2013), 1521–1553.