A map between moduli spaces of connections - Archive ouverte HAL Access content directly
Journal Articles Symmetry, Integrability and Geometry : Methods and Applications Year : 2020

A map between moduli spaces of connections

Frank Loray
Valente Ramirez
  • Function : Author
  • PersonId : 1030599

Abstract

We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to lift such connections to an elliptic curve. The transformation is as follows: given an elliptic curve C with elliptic quotient π : C → P 1 , and the logarithmic connection (E, ∇) on P 1 , we may pullback the connection to the elliptic curve to obtain a new connection (π * E, π * ∇) on C. After suitable birational modifications we bring the connection to a particular normal form. The whole transformation is equivariant with respect to bundle automorphisms and therefore defines a map between the corresponding moduli spaces of connections. The aim of this paper is to describe the moduli spaces involved and compute explicit expressions for the above map in the case where the target space is the moduli space of rank 2 logarithmic connections on an elliptic curve C with two simple poles and trivial determinant.
Fichier principal
Vignette du fichier
map-ms-SIGMA.pdf (941.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02338280 , version 1 (29-10-2019)
hal-02338280 , version 2 (18-06-2020)
hal-02338280 , version 3 (14-10-2020)
hal-02338280 , version 4 (02-12-2020)

Identifiers

Cite

Frank Loray, Valente Ramirez. A map between moduli spaces of connections. Symmetry, Integrability and Geometry : Methods and Applications, 2020, 16, pp.article n° 125. ⟨10.3842/SIGMA.2020.125⟩. ⟨hal-02338280v4⟩
130 View
80 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More