Rational equivalence and Lagrangian tori on K3 surfaces

  • Nick Sheridan

    University of Edinburgh, UK
  • Ivan Smith

    University of Cambridge, UK
Rational equivalence and Lagrangian tori on K3 surfaces cover

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Abstract

Fix a symplectic K3 surface homologically mirror to an algebraic K3 surface by an equivalence taking a graded Lagrangian torus to the skyscraper sheaf of a point . We show there are Lagrangian tori with vanishing Maslov class in 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 , and fits into a conjectural relationship between Lagrangian cobordism and rational equivalence of algebraic cycles.

Cite this article

Nick Sheridan, Ivan Smith, Rational equivalence and Lagrangian tori on K3 surfaces. Comment. Math. Helv. 95 (2020), no. 2, pp. 301–337

DOI 10.4171/CMH/489