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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Ross and Thomas introduced the concept of slope stability to study  K ‐stability, which has conjectural relation with the existence of constant scalar curvature Kähler metric. This paper presents a study of slope stability of Fano manifolds of dimension  n ⩾3 with respect to smooth curves. The question turns out to be easy for curves of genus at least 1 and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold ( X ,− K   X  ) is not slope stable with respect to a smooth curve. Our result also states that a Fano three‐fold  X  with Picard number 1 is slope stable with respect to every smooth curve unless  X  is the projective space.

Slopes of smooth curves on Fano manifolds