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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider elliptic surfaces $\mathcal{E}$ over a field $k$ equipped withzero section $O$ and another section $P$ of infinite order. If $k$ hascharacteristic zero, we show there are only finitely many points where $O$ istangent to a multiple of $P$. Equivalently, there is a finite list of integerssuch that if $n$ is not divisible by any of them, then $nP$ is not tangent to$O$. Such tangencies can be interpreted as unlikely intersections. If $k$ hascharacteristic zero or $p>3$ and $\mathcal{E}$ is very general, then we showthere are no tangencies between $O$ and $nP$. We apply these results tosquare-freeness of elliptic divisibility sequences and to geography ofsurfaces. In particular, we construct mildly singular surfaces of arbitraryfixed geometric genus with $K$ ample and $K^2$ unbounded.

Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces