Uniform bounds for torsion packets on tropical curves

Abstract: Say two points x, y on an algebraic curve are in the same torsion packet if [x - y] is a torsion element of the Jacobian. In genus 0 and 1, torsion packets have infinitely many points. In higher genus, a theorem of Raynaud states that all torsion packets are finite. It was long conjectured, and only recently proven*, that the size of a torsion packet is bounded uniformly in terms of the genus of the underlying curve. We study the tropical analogue of this construction for a metric graph. On a higher genus metric graph, torsion packets are not always finite, but they are finite under an additional "genericity" assumption on the edge lengths. Under this genericity assumption, the torsion packets satisfy a uniform bound in terms of the genus of the underlying graph. (*by Kuehne and Looper-Silverman-Wilmes in 2021)

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

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Videos of some past talks are available on YouTube here, while some slides can be found here.