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Special Cubic Four-Folds, K3 Surfaces, and the Franchetta Property
- Source :
- International Mathematics Research Notices, 1-31, STARTPAGE=1;ENDPAGE=31;ISSN=1073-7928;TITLE=International Mathematics Research Notices, International Mathematics Research Notices, pp. 1-31
- Publication Year :
- 2023
-
Abstract
- O’Grady conjectured that the Chow group of 0-cycles of the generic fiber of the universal family over the moduli space of polarized K3 surfaces of genus $g$ is cyclic. This so-called generalized Franchetta conjecture has been solved only for low genera where there is a Mukai model (precisely, when $g\leq 10$ and $g=12, 13, 16, 18, 20$), by the work of Pavic–Shen–Yin. In this paper, as a non-commutative analogue, we study the Franchetta property for families of special cubic four-folds (in the sense of Hassett) and relate it to O’Grady’s conjecture for K3 surfaces. Most notably, by using special cubic four-folds of discriminant 26, we prove O’Grady’s generalized Franchetta conjecture for $g=14$, providing the first evidence beyond Mukai models.
- Subjects :
- General Mathematics
Mathematics
Subjects
Details
- ISSN :
- 10737928
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices, 1-31, STARTPAGE=1;ENDPAGE=31;ISSN=1073-7928;TITLE=International Mathematics Research Notices, International Mathematics Research Notices, pp. 1-31
- Accession number :
- edsair.doi.dedup.....6173d417fa7848d67ff8a97e2b8f64f1