Rational equivalence and Lagrangian tori on K3 surfaces

Nick Sheridan, Ivan Smith

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)301–337
Number of pages30
JournalCommentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society (CMH)
Issue number2
Early online date16 Jun 2020
Publication statusPublished - 30 Jun 2020


Dive into the research topics of 'Rational equivalence and Lagrangian tori on K3 surfaces'. Together they form a unique fingerprint.

Cite this