Speaker: Matthew Huynh
Location: Math 5-127
Abstract:
Let X be a smooth, complex projective variety, let V be a vector bundle of rank d on X, and let G be a connected, reductive group.
First, we introduce the Hitchin morphism from the moduli space of V-valued G-Higgs bundles on X to the Hitchin base. Next, we explain the Chen-Ngô Conjecture, which predicts that the image of the Hitchin morphism when V is the bundle of holomorphic 1-forms is the so-called space of spectral data.
We verify the Chen-Ngô Conjecture whenever X is a ruled surface, or a smooth modification of a non-isotrivial elliptic fibration with only reduced fibers. Furthermore, we show that if in addition G is a classical group, then the space of spectral data is surjected upon by the moduli space of semiharmonic G-Higgs bundles.
