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

2025/11/21 by Yuan Lu, Lu, Yuan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.16875

openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/28

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.

Citations

• Special cubic fourfolds, K3 surfaces and the Franchetta property
• On O'Grady's generalized Franchetta conjecture
• Moduli of sheaves and the Chow group of K3 surfaces
• Log canonical models for the moduli space of curves: First divisorial contraction
• Constructions of nontautological classes on moduli spaces of curves
• Calculating cohomology groups of moduli spaces of curves via algebraic geometry

Related

• On O'Grady's generalized Franchetta conjecture
• A remark on the generalized Franchetta conjecture for K3 surfaces
• Special cubic fourfolds, K3 surfaces and the Franchetta property
• The generalized Franchetta conjecture for some hyper-Kähler varieties
• Deligne-Beilinson cohomology of the universal K3 surface