Thomas Bouchet

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math.AG2026

Functionality for isomorphism classes of curves and hypersurfaces

Thomas Bouchet, Reynald Lercier, Jeroen Sijsling +1

We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author…

math.AG2025

Mumford-type Shimura curves contained in the Torelli locus

Thomas Bouchet, Jeroen Hanselman, Andreas Pieper +1

In this article we give explicit equations for two Shimura families of genus 4 curves whose Jacobians are abelian fourfolds of Mumford type. These are the first explicit examples o…

math.AG2025

Heuristics for (ir)reducibility of $p$ -rank strata of the moduli space of hyperelliptic curves

Thomas Bouchet, Erik Davis, Steven R. Groen +2

Let $H_{g}$ denote the moduli space of smooth hyperelliptic curves of genus $g$ in characteristic $p \geq 3$ , and let $H_{g}^{f}$ denote the $p$ -rank $f$ stratum of $\…

Functionality for isomorphism classes of curves and hypersurfaces

Mumford-type Shimura curves contained in the Torelli locus

Heuristics for (ir)reducibility of p-rank strata of the moduli space of hyperelliptic curves

Heuristics for (ir)reducibility of $p$ -rank strata of the moduli space of hyperelliptic curves