Journal of the Mathematical Society of Japan

Derived equivalence of Ito–Miura–Okawa–Ueda Calabi–Yau 3-folds


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


We prove derived equivalence of Calabi–Yau threefolds constructed by Ito–Miura–Okawa–Ueda as an example of non-birational Calabi–Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.


I was partially supported by the Russian Academic Excellence Project “5-100”, by RFBR grants 14-01-00416, 15-01-02164, 15-51-50045, and by the Simons Foundation.

Article information

J. Math. Soc. Japan, Volume 70, Number 3 (2018), 1007-1013.

Received: 9 December 2016
First available in Project Euclid: 18 June 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]

derived equivalences Calabi–Yau threefolds simple group of type ${\boldsymbol{G}}_2$ mutations


KUZNETSOV, Alexander. Derived equivalence of Ito–Miura–Okawa–Ueda Calabi–Yau 3-folds. J. Math. Soc. Japan 70 (2018), no. 3, 1007--1013. doi:10.2969/jmsj/76827682.

Export citation


  • T. Bridgeland, Equivalences of triangulated categories and Fourier–Mukai transforms, Bull. London Math. Soc., 31 (1999), 25–34.
  • 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 preprint arXiv:1606.04210.
  • M. Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math., 92 (1988), 479–508.
  • A. Kuznetsov, Hyperplane sections and derived categories, Izv. Ross. Akad. Nauk Ser. Mat., 70 (2006), 23–128 (in Russian); translation in Izv. Math., 70 (2006), 447–547.