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

In this paper, we study the problem of tropicalizing tame degree threecoverings of the projective line. Given any degree three covering$C\longrightarrow{\mathbb{P}^{1}}$, we give an algorithm that produces theBerkovich skeleton of $C$. In particular, this gives an algorithm for findingthe Berkovich skeleton of a genus $3$ curve. The algorithm uses a continuitystatement for inertia groups of semistable Galois coverings, which we provefirst. After that we give a formula for the decomposition group of anirreducible component $\Gamma\subset{\mathcal{C}_{s}}$ for a semistable Galoiscovering $\mathcal{C}\longrightarrow{\mathcal{D}}$. We conclude the paper witha simple application of these $S_{3}$-coverings to elliptic curves, givinganother proof of the familiar semistability criterion for elliptic curves usinga natural degree three morphism to $\mathbb{P}^{1}$ instead of the usual degreetwo morphism.

Tropicalizing tame degree three coverings of the projective line