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

We classify linearly normal surfaces $S \subset \mathbf{P}^{r+1}$ of degree$d$ such that $4g-4 \leq d \leq 4g+4$, where $g>1$ is the sectional genus (itis a classical result that for larger $d$ there are only cones). We apply thisto the study of the extension theory of pluricanonical curves and genus $3$curves, whenever they verify Property $N_2$, using and slightly expanding thetheory of integration of ribbons of the authors and E.~Sernesi. We compute thecorank of the relevant Gaussian maps, and we show that all ribbons over suchcurves are integrable, and thus there exists a universal extension.  We carry out a similar program for linearly normal hyperelliptic curves ofdegree $d\geq 2g+3$. We classify surfaces having such a curve $C$ as ahyperplane section, compute the corank of the relevant Gaussian maps, and provethat all ribbons over $C$ are integrable if and only if $d=2g+3$. In the lattercase we obtain the existence of a universal extension.

Extensions of curves with high degree with respect to the genus