Journal of the Mathematical Society of Japan

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

Alexander KUZNETSOV

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Abstract

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.

Note

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1529309021

Digital Object Identifier
doi:10.2969/jmsj/76827682

Mathematical Reviews number (MathSciNet)
MR3830796

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1529309021


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References

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