# Elisa Lorenzo Garcia: On different expressions for invariants of hyperelliptic curves of genus 3

arXiv: https://arxiv.org/abs/1907.05776

**Time: **
Wed 2020-03-11 13.15 - 14.15

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

**Lecturer: **
Elisa Lorenzo Garcia, University Rennes 1

### Abstract

In this talk, we will give a passage formula between different invariants of genus 3 hyperelliptic curves: in particular between Tsuyumine and Shioda invariants. This is needed to get modular expressions for Shioda invariants.

On the other hand, we will also get Shioda invariants described in terms of differences of roots of the equation defining the hyperelliptic curve: this has applications for studying the reduction type of the curve. Under certain conditions on its jacobians, we will give a criterion for determining the type of bad reduction of a genus 3 hyperelliptic curve.