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

We prove that for every smooth prime Fano 3‐fold  V , the Hilbert schemeHilb   s  cV    of smooth connected curves on  V  contains a generically non‐reduced irreducible component of Mumford type. We also study the deformations of degenerate curves  C  in  V , i.e., curves  C  contained in a smooth anticanonical memberS  ∈  |  −    K  V    |of  V . We give a sufficient condition for  C  to be stably degenerate, i.e., every small (and global) deformation of  C  in  V  is contained in a deformation of  S  in  V . As a result, by using the Hilbert‐flag scheme of  V , we determine the dimension and the smoothness ofHilb   s  cV    at the point [ C ], assuming that the class of  C  in    Pic  S    is generated by    h  :  =  −   K  V    |  Stogether with the class of a line, or a conic on  V .

Obstructions to deforming curves on a prime Fano 3‐fold