Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The class of the affine line is a zero divisor in the Grothendieck ring: Via $ G _{ 2 }$-Grassmannians


Authors: Atsushi Ito, Makoto Miura, Shinnosuke Okawa and Kazushi Ueda
Journal: J. Algebraic Geom. 28 (2019), 245-250
DOI: https://doi.org/10.1090/jag/731
Published electronically: December 6, 2018
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Abstract | References | Additional Information

Abstract: Motivated by [J. Algebraic Geom. 27 (2018), pp. 203-209] and [C. R. Math.Acad. Sci. Paris 354 (2016), pp. 936-939], we show the equality $ \left ( [ X ] - [ Y ] \right ) \cdot [ \mathbb{A} ^{ 1 } ] = 0 $ in the Grothendieck ring of varieties, where $ ( X, Y ) $ is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type $ G _{ 2 } $.


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Additional Information

Atsushi Ito
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: aito@math.kyoto-u.ac.jp

Makoto Miura
Affiliation: Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea
Email: miura@kias.re.kr

Shinnosuke Okawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
Email: okawa@math.sci.osaka-u.ac.jp

Kazushi Ueda
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email: kazushi@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/jag/731
Received by editor(s): July 23, 2016
Published electronically: December 6, 2018
Additional Notes: The first author was supported by the Grant-in-Aid for JSPS fellows, No. 26–1881. A part of this work was done when the second author was supported by Frontiers of Mathematical Sciences and Physics at University of Tokyo. The second author was also supported by Korea Institute for Advanced Study. The third author was partially supported by Grants-in-Aid for Scientific Research (16H05994, 16K13746, 16H02141, 16K13743, 16K13755, 16H06337) and the Inamori Foundation. The fourth author was partially supported by Grants-in-Aid for Scientific Research (24740043, 15KT0105, 16K13743, 16H03930).
Article copyright: © Copyright 2018 University Press, Inc.