English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

LetX⊂ℙ4{X\subset\mathbb{P}^{4}}be a very general hypersurface of degreed≥6{d\geq 6}. Griffiths and Harris conjectured in 1985 that the degree of every curveC⊂X{C\subset 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 beingd=5005{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 overℚ{\mathbb{Q}}that satisfy the conjecture.

On the degree of algebraic cycles on hypersurfaces