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complete curves 1complex algebraic geometry 1computational algebra 1genus 1moduli space of curves 1

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math.NT2026

Refined Humbert invariants and subvarieties of $\Ac_2(\C)$: the rank 3 case

Elisa Lorenzo García, Christophe Ritzenthaler

Over the complex field, we show that the principally polarised abelian surfaces with a given refined Humbert invariant of rank 3 are all Galois conjugated.

math.NT2024

An arithmetic intersection for squares of elliptic curves with complex multiplication

Elisa Lorenzo García, Christophe Ritzenthaler, Fernando Rodríguez Villegas

Let be a genus curve with Jacobian isomorphic to the square of an elliptic curve with complex multiplication by a maximal order in an imaginary quadratic field of discrimin…

math.NT2024

Siegel modular forms of degree three and invariants of ternary quartics

Reynald Lercier, Christophe Ritzenthaler

We determine the structure of the graded ring of Siegel modular forms of degree 3. It is generated by 19 modular forms, among which we identify a homogeneous system of parameters w…