Parabolic Hecke Eigensheaves
Ron Donagi, Tony Pantev, "Parabolic Hecke Eigensheaves"
English | ISBN: 2856299601 | 2022 | 192 pages | PDF | 3 MB
English | ISBN: 2856299601 | 2022 | 192 pages | PDF | 3 MB
Abstract. — We study the Geometric Langlands Conjecture (GLC) for rank two flat
bundles on the projective line C with tame ramification at five points {p1, p2, p3, p4, p5}.
In particular we construct the automorphic D-modules predicted by GLC on the
moduli space of rank two parabolic bundles on (C, {p1, p2, p3, p4, p5}). The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers
of the Hitchin fibration to reduce the problem to one in classical projective geometry
on the intersection of two quadrics in P4.