3 papers
math.AG2026
Equations of genus curves from their theta constants
Jeroen Hanselman, Andreas Pieper, Sam Schiavone
In this article we give explicit formulas for the equations of a generic genus curve in terms of its theta constants. The method uses the Prym construction and the beautiful cl…
math.NT2026
The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7
Raymond van Bommel, Edgar Costa, Noam D. Elkies +3
We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, iso…
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…