We study the geometry and arithmetic of the curves $ C\colon y^ 3= x^ 4+ ax^ 2+ b $ and
their associated Prym abelian surfaces $ P $. We prove a Torelli theorem in this context and …

We study a 3-dimensional stratum ℳ 3, V of the moduli space ℳ 3 of curves of genus 3
parameterizing curves Y that admit a certain action of V= C 2× C 2. We determine the …

Abstract Let C∕ K be a smooth plane quartic over a discrete valuation field. We characterize
the type of reduction (ie, smooth plane quartic, hyperelliptic genus 3 curve or bad) over K in …

We give a conjectural characterisation of the stable reduction of plane quartics over local
fields in terms of their Cayley octads. This results in p-adic criteria that efficiently give the …

We prove an inequality between the conductor and the discriminant for all hyperelliptic
curves defined over discretely valued fields with perfect residue field of characteristic not …

We give bounds on the primes of geometric bad reduction for curves of genus $3 $ of
primitive complex multiplication (CM) type in terms of the CM orders. In the case of elliptic …

In this paper we give a passage formula between different invariants of genus 3 hyperelliptic
curves: in particular between Tsuyumine and Shioda invariants. This is needed to get …

Let $ C $ be a smooth projective curve, and let $ J $ be its Jacobian. We prove vanishing
criteria for the Ceresa cycle $\kappa (C)\in\mathrm {CH} _1 (J)\otimes\mathbb {Q} $ in the …

We describe algorithms to represent and compute groups of Hecke characters. We make
use of an idèlic point of view and obtain the whole family of such characters, including …

In this paper we determine the conductor exponent of non-special Ciani quartics at primes of
potentially good reduction in terms of the Ciani invariants. As an intermediate step in order to …