PreprintCC BY-SA 4.0arXiv
Rationally connectedness and O'Grady's generalized Franchetta conjecture for K3 surfaces
Abstract
O'Grady's generalized Franchetta conjecture asks whether any codimension two cycle on the universal polarized K3 surfaces restricts to a multiple of the Beauville--Voisin class on a given K3 surface. We apply Bergeron--Li's result on the cohomology of universal K3 surfaces to give an affirmative answer to this conjecture when the universal K3 surface is rationally connected, including the case of genus 22.
Related
- Mathematical Characterization of Dynamic Risk Spillovers in Carbon-Energy Financial Networks with Multi-Dimensional Uncertainty: A TVP-VAR-DY Connectedness Approach via Generalized Forecast-Error Variance Decomposition
- Generalized Iskovskikh surfaces and unirationality of del Pezzo surfaces of degree $2$
- Orlov's rationality conjecture for surfaces
- Generalised Cone Conjecture, III: Non-generic Sakai surfaces
- Topping's diameter conjecture for immersed surfaces
BibTeX
@misc{lu2026rationally,
title = {{Rationally connectedness and O'Grady's generalized Franchetta conjecture for K3 surfaces}},
author = {Yuan Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36909},
eprint = {2609.36909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36909},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Rationally connectedness and O'Grady's generalized Franchetta conjecture for K3 surfaces
AU - Yuan Lu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36909
UR - https://arxiv.org/abs/2609.36909
AB - O'Grady's generalized Franchetta conjecture asks whether any codimension two cycle on the universal polarized K3 surfaces restricts to a multiple of the Beauville--Voisin class on a given K3 surface. We apply Bergeron--Li's result on the cohomology of universal K3 surfaces to give an affirmative answer to this conjecture when the universal K3 surface is rationally connected, including the case of genus 22.
ER -