On O'Grady's generalized Franchetta conjecture for genus 11 K3 surfaces

TL;DR

This paper proves O'Grady's generalized Franchetta conjecture for genus 11 K3 surfaces by combining Mukai's program and results on the Chow group of moduli spaces.

Contribution

It provides the first affirmative proof of the conjecture for genus 11 K3 surfaces, utilizing advanced geometric and Chow group techniques.

Findings

Confirmed the conjecture for genus 11 K3 surfaces

Connected Mukai's program with Chow group generation

Extended understanding of algebraic cycles on K3 surfaces

Abstract

O'Grady's generalized Franchetta conjecture asks whether any codimension two cycle on the universal polarized K3 surface restricts to a multiple of the Beauville--Voisin class on a given K3 surface. We apply Mukai's program for genus 11 curves and K3 surfaces, together with a result on the tautological generation of the second Chow group of the moduli space of curves, to give an affirmative answer to this conjecture in genus 11.