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 consider surfaces with a double elliptic fibration, with two sections. Westudy the orbits under the induced translation automorphisms proving that,under natural conditions, the finite orbits are confined to a curve. This goesin a similar direction of (and is motivated by) recent work by Cantat-Dujardin,although we use very different methods and obtain related but differentresults. As a sample of application of similar arguments, we prove a new caseof the Zilber-Pink conjecture, namely Theorem 1.5, for certain schemes over a2-dimensional base, which was known to lead to substantial difficulties. Mostresults rely, among other things, on recent theorems by Bakker and the secondauthor of `Ax-Schanuel Type'; we also relate a functional condition with atheorem of Shioda on ramified sections of the Legendre scheme. For one of ourproofs, we also use recent height inequalities by Yuan-Zhang. Finally, in anappendix, we show that the Relative Manin-Mumford Conjecture over the complexnumber field is equivalent to its version over the field of algebraic numbers.

Finite Orbits in Surfaces with a Double Elliptic Fibration and Torsion Values of Sections