Curves and cycles on K3 surfaces

By D. Huybrechts, Claire Voisin. 2013

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c06126b50eb18f5c096d0b32ec0a8b641692ac64

How researchers see this paper

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In Algebra and Number Theory

1. D. Huybrechts
2. Claire Voisin
3. G. Farkas
4. M. Aprodu
5. Mihnea Cristian Popa
6. Yinan Song
7. D. Joyce

In Geometry and Topology

1. D. Huybrechts
2. Claire Voisin
3. Kieran G. O’Grady
4. E. Markman
5. P. Stellari
6. Ulrike Riess
7. G. Farkas
8. Emanuele Macrì

In Mathematical Physics

1. D. Huybrechts
2. Claire Voisin
3. P. Stellari
4. E. Markman
5. Emanuele Macrì
6. Ulrike Riess
7. Alexander Perry
8. G. Farkas

Citations in the corpus

• Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties (2015, background): “The variety Z is by definition a “constant cycle subvariety” in the sense of Huybrechts [14].”
• Lectures on K3 Surfaces (2016, background): “Curves with this property have been introduced as constant cycle curves in [260].”