Personal tools
You are here: Home Publications Curves and cycles on K3 surfaces

Curves and cycles on K3 surfaces

Daniel Huybrechts, with an appendix by Claire Voisin

Number 22
Author Daniel Huybrechts
Year 2013

The notion of constant cycle curves on K3 surfaces is introduced. These are curves that do not contribute to the Chow group of the ambient K3 surface. Rational curves are the most prominent examples.
We show that constant cycle curves behave in some respects like rational curves. E.g. using Hodge theory one finds that in each linear system there are at most finitely many such curves of bounded order.
Over finite fields, any curve is expected to be a constant cycle curve, whereas over number fields this does not hold. The relation to the Bloch--Beilinson conjectures for K3 surfaces over global fields is discussed.

More information about this publication…

Document Actions
March 2020 »
March
MoTuWeThFrSaSu
1
2345678
9101112131415
16171819202122
23242526272829
3031