Decomposition of the small diagonal for families of K3 surfaces

Qizheng Yin

Using ideas and techniques from Gromov-Witten theory, we obtain a decomposition of the third small diagonal for the universal (quasi-)polarized K3 surface, thus generalizing a theorem of Beauville-Voisin for a fixed K3 surface. As a result, we prove a conjecture of Marian-Oprea-Pandharipande: that the tautological ring of the moduli of (quasi-)polarized K3 surfaces is generated by (the classes of) the Noether-Lefschetz loci. Joint work with Rahul Pandharipande.

http://scgp.stonybrook.edu/video_portal/video.php?id=2817

Simons- Workshop: Derived categories and Chow groups of hyperkaehler and Calabi-Yau varieties