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arXiv · 1809.03892

Rational equivalence and Lagrangian tori on K3 surfaces

Nick Sheridan·Ivan Smith
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Abstract

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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Nick Sheridan, Ivan Smith. 2018-09-11. Rational equivalence and Lagrangian tori on K3 surfaces. https://doi.org/10.4171/cmh/489

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