On the moduli of logarithmic connections on elliptic curves

Thiago Fassarella (1) , Frank Loray (2) , Alan Muniz (3)

1 UFF - Universidade Federal Fluminense [Rio de Janeiro]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 UFES - Universidade Federal do Espirito Santo

We describe moduli spaces of logarithmic rank 2 connections on elliptic curves with n>0 poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze the underlying parabolic bundles; their stability and instability play a major role.

Domaines: Analyse classique [math.CA]; Géométrie algébrique [math.AG]

Thiago Fassarella, Frank Loray, Alan Muniz. On the moduli of logarithmic connections on elliptic curves. Mathematische Zeitschrift, In press, ⟨10.1007/s00209-022-03041-4⟩. ⟨hal-02923926v3⟩