(TE)-structures over the irreducible 2-dimensional globally nilpotent F-manifold germ

Abstract

We find formal and holomorphic normal forms for a class of meromorphic connections (the so-called $(TE)$-structures) over the irreducible $2$-dimensional globally nilpotent $F$-manifold germ ${\mathcal{N}}_2$. We find normal forms for Euler fields on ${\mathcal{N}}_2$ and we characterize the Euler fields on ${\mathcal{N}}_2$ which are induced by a $(TE)$-structure.

abstract shortened; introduction expanded; other minor modifications with respect to the previous version; 53 pages

References in corpus (2)

• Dubrovin's duality for $F$-manifolds with eventual identities
• (T)-structures over 2-dimensional F-manifolds: formal classification

Cited by in corpus (1)

• Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1