27.06.2025
A modular interpretation of the Hessian of elliptic curves
Abstract
In this talk, we will discuss the modular interpretation of the Hessian transformation on elliptic curves. We begin by recalling some classical results concerning the action of the Hessian transforma-tion on the j-invariants and on the Hesse pencil, and we rephrase them in the context of the modu-lar curves X(1) and X(3). Building on the work of Mula, Pintore, and Taufer in the recent preprint (ArXiv:2407.17042), we lift the Hessian transformation up to maps on 16 different modular curves, in-cluding X(6), and analyse their effects on the associated moduli spaces. Finally, we give a numerical representation of Hessian map on the extended complex upper half-plane H∗. This talk is based on the speaker’s Master’s thesis supervised by Pintore, Taufer and Mula.
Bio
Riccardo Lolato — Master’s degree in Mathematics - Cryptography, Universita` degli Studi di Trento.
Photo provided by speaker
In this talk, we will discuss the modular interpretation of the Hessian transformation on elliptic curves. We begin by recalling some classical results concerning the action of the Hessian transforma-tion on the j-invariants and on the Hesse pencil, and we rephrase them in the context of the modu-lar curves X(1) and X(3). Building on the work of Mula, Pintore, and Taufer in the recent preprint (ArXiv:2407.17042), we lift the Hessian transformation up to maps on 16 different modular curves, in-cluding X(6), and analyse their effects on the associated moduli spaces. Finally, we give a numerical representation of Hessian map on the extended complex upper half-plane H∗. This talk is based on the speaker’s Master’s thesis supervised by Pintore, Taufer and Mula.
Bio
Riccardo Lolato — Master’s degree in Mathematics - Cryptography, Universita` degli Studi di Trento.
Photo provided by speaker