K3曲面上的有理等价和拉格朗日环面

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2018-09-11 DOI:10.4171/CMH/489

Nick Sheridan, I. Smith

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引用次数: 5

摘要

通过将X中的一个梯度拉格朗日环面L与Y点Y的摩天楼束等价，将一个对称的K3曲面X与代数的K3曲面Y同构固定。我们证明了在X中存在消失的Maslov类的拉格朗日环面，其在Fukaya范畴的Grothendieck群中的类不是由拉格朗日球生成的。这与关于Y的Chow群中的“Beauville—Voisin子带”的说法是一致的，并且符合拉格朗日协同性与代数循环的有理等价之间的推测关系。

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Rational equivalence and Lagrangian tori on K3 surfaces

Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L in X to the skyscraper sheaf of a point y of Y. We show there are Lagrangian tori with vanishing Maslov class in X whose class in the Grothendieck group of the Fukaya category is not generated by Lagrangian spheres. This is mirror to a statement about the `Beauville--Voisin subring' in the Chow groups of Y, and fits into a conjectural relationship between Lagrangian cobordism and rational equivalence of algebraic cycles.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.