Title: Optimum weight chamber examples of moduli spaces of stable parabolic bundles in genus 0,
Abstract: We present an explicit construction of the moduli spaces of rank 2 stable
parabolic bundles of parabolic degree 0 over the Riemann sphere, corresponding
to "optimum" open weight chambers of parabolic weights in the weight polytope.
The complexity of the different moduli space' weight chambers is understood in
terms of the complexity of the actions of the corresponding groups of bundle
automorphisms on stable parabolic structures. For the given choices of
parabolic weights, $\mathscr{N}$ consists entirely of isomorphism classes of
strictly stable parabolic bundles whose underlying Birkhoff-Grothendieck
splitting coefficients are constant and minimal, is constructed as a quotient
of a set of stable parabolic structures by a group of bundle automorphisms, and
is a smooth, compact complex manifold biholomorphic to
$\left(\mathbb{C}\mathbb{P}^{1}\right)^{n-3}$ for even degree, and
$\mathbb{C}\mathbb{P}^{n-3}$ for odd degree. As an application of the
construction of such explicit models, we provide an explicit characterization
of the nilpotent cone locus on $T^{*}\mathscr{N}$ for Hitchin's integrable
system.