Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type

Fu L, Laterveer R, Vial C (2021)
Annali di Matematica Pura ed Applicata.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Fu, Lie; Laterveer, Robert; Vial, CharlesUniBi
Abstract / Bemerkung
Given a smooth projective variety, a Chow-Kunneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kahler varieties admit a multiplicative Chow-Kunneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kahler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow-Kunneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Kuchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow-Kunneth decomposition, by establishing this for two families of Todorov surfaces.
Stichworte
Algebraic cycles; Chow groups; Motives; K3 surfaces; Cubic; hypersurfaces; Fano varieties of lines; Franchetta conjecture; Hyper-Kahler varieties; Beauville
Erscheinungsjahr
2021
Zeitschriftentitel
Annali di Matematica Pura ed Applicata
ISSN
0373-3114
eISSN
1618-1891
Page URI
https://pub.uni-bielefeld.de/record/2955694

Zitieren

Fu L, Laterveer R, Vial C. Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type. Annali di Matematica Pura ed Applicata. 2021.
Fu, L., Laterveer, R., & Vial, C. (2021). Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type. Annali di Matematica Pura ed Applicata. https://doi.org/10.1007/s10231-021-01070-0
Fu, L., Laterveer, R., and Vial, C. (2021). Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type. Annali di Matematica Pura ed Applicata.
Fu, L., Laterveer, R., & Vial, C., 2021. Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type. Annali di Matematica Pura ed Applicata.
L. Fu, R. Laterveer, and C. Vial, “Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type”, Annali di Matematica Pura ed Applicata, 2021.
Fu, L., Laterveer, R., Vial, C.: Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type. Annali di Matematica Pura ed Applicata. (2021).
Fu, Lie, Laterveer, Robert, and Vial, Charles. “Multiplicative Chow-Kunneth decompositions and varieties of cohomological K3 type”. Annali di Matematica Pura ed Applicata (2021).

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar