TY - JOUR

T1 - The class of the affine line is a zero divisor in the Grothendieck ring

T2 - Via G 2 -Grassmannians

AU - Ito, Atsushi

AU - Miura, Makoto

AU - Okawa, Shinnosuke

AU - Ueda, Kazushi

N1 - Funding Information:
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). This joint work started with a discussion between the second and third authors at the Korea Institute for Advanced Study. The third author is indebted to Seung-Jo Jung for the invitation. The authors thank Kiwamu Watanabe for answering their question on homogeneous varieties, Sergey Galkin for various useful comments, and Grzegorz Kapustka and Micha l Kapustka for pointing out the reference [KK16]. The authors also thank Takehiko Yasuda for communicating the paper [Nic11] to them and the anonymous referees for providing a number of valuable comments and for suggesting a simpler proof of Proposition 2.3.
Funding Information:
Received July 23, 2016. 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).
Publisher Copyright:
© 2018 University Press, Inc.

PY - 2018

Y1 - 2018

N2 - 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 ([X] − [Y ])·[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 .

AB - 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 ([X] − [Y ])·[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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U2 - 10.1090/jag/731

DO - 10.1090/jag/731

M3 - Article

AN - SCOPUS:85064720832

SN - 1056-3911

VL - 28

SP - 245

EP - 250

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

IS - 2

ER -