Rational equivalence and Lagrangian tori on K3 surfaces

Nick Sheridan, Ivan Smith

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)301–337
Number of pages30
JournalCommentarii Mathematici Helvetici
Volume95
Issue number2
Early online date16 Jun 2020
DOIs
Publication statusPublished - 30 Jun 2020

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