Table of contents

  • This session has been presented October 10, 2014.

Description

  • Speaker

    Enea Milio - Université Bordeaux I

Nous nous proposons de décrire nos travaux de thèse sur le calcul des polynômes modulaires en genre 2. Ces polynômes dépendent des invariants d'Igusa, qui sont une généralisation de la fonction j dans le genre 1, et permettent d'obtenir toutes les variétés abéliennes isogènes à une variété abélienne donnée. Dans un premier temps, nous reviendrons sur cette notion de polynôme en genre 1 et 2 et discuterons de leur calcul par une approche du type évaluation/interpolation. Dans un second temps, nous expliquerons comment généraliser ces polynômes à d'autres invariants et décrirons certaines de leurs propriétés, notamment le lien entre le dénominateur d'un coefficient du polynôme modulaire et les surfaces de Humbert.

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