Higgs bundles for Hecke eigensheaves in rank 2 and genus 2
Apparaît dans la collection : Families of Kähler spaces / Familles d'espaces kählériens
We'll discuss our joint work with Ron Donagi and Tony Pantev on the construction of the Higgs bundles associated to Hecke eigensheaves for the geometric Langlands program in the case of rank 2 local systems on a curve of genus 2 . Recall that the moduli space of bundles in this case has two connected components: $\mathbb{P}^3$ and the intersection of two quadrics in $\mathbb{P}^5$. We look for Higgs bundles on these spaces with parabolic structure and logarithmic poles along the wobbly locus. This leads to the study of the geometry of the wobbly locus and its singularities, and the use of our Dolbeault higher direct image construction for the calculation of Hecke operators.
