The class of the affine line is a zero divisor in the Grothendieck ring: Via 𝐺₂-Grassmannians

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2018-12-06 DOI:10.1090/JAG/731

Atsushi Ito, Makoto Miura, Shinnosuke Okawa, K. Ueda

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引用次数: 0

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 ( [ X ] − [ Y ] ) ⋅ [ A 1 ] = 0 \left ( [ X ] - [ Y ] \right ) \cdot [ \mathbb {A} ^{ 1 } ] = 0 in the Grothendieck ring of varieties, where ( X , Y ) ( X, Y ) is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type G 2 G _{ 2 } .

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仿射线的类是Grothendieck环上的零因子:通过𝐺₂-Grassmannians

[J]代数几何，27 (2018)，pp. 203-209 [j]。r .数学。学会科学。(Paris 354 (2016)， pp. 936-939)，我们证明了在Grothendieck环上的等式([X]−[Y])⋅[A 1] = 0 \left ([X] - [Y] \right) \cdot [\mathbb {A} ^{1}] = 0，其中(X, Y) (X，Y)是一对从G 2 G _{2}型格拉斯曼人身上剪下来的卡拉比-丘三褶。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.