On the degree of algebraic cycles on hypersurfaces

Publikation: Arbeitspapier/Preprint › Preprint

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  • Matthias Paulsen

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OriginalspracheEnglisch
Seitenumfang12
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 13 Sept. 2021

Abstract

Let X⊂ℙ4 be a very general hypersurface of degree d≥6. Griffiths and Harris conjectured in 1985 that the degree of every curve C⊂X is divisible by d. Despite substantial progress by Kollár in 1991, this conjecture is not known for a single value of d. Building on Kollár's method, we prove this conjecture for infinitely many d, the smallest one being d=5005. The set of these degrees d has positive density. We also prove a higher-dimensional analogue of this result and construct smooth hypersurfaces defined over ℚ that satisfy the conjecture.

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On the degree of algebraic cycles on hypersurfaces. / Paulsen, Matthias.
2021.

Publikation: Arbeitspapier/Preprint › Preprint

Paulsen M. On the degree of algebraic cycles on hypersurfaces. 2021 Sep 13. Epub 2021 Sep 13. doi: 10.48550/arXiv.2109.06303
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