On vector bundles over algebraic and arithmetic curves (original) (raw)

The paper examines vector bundles over algebraic and arithmetic curves, focusing on two main contexts: parabolic bundles over smooth projective curves and metrized bundles in Arakelov geometry over arithmetic curves. The first part addresses the Boden-Hu conjecture concerning the desingularization of the moduli scheme of semistable parabolic bundles, demonstrating that it holds for bundles of rank up to eight. The second part draws an analogy to Arakelov bundles and explores the existence of such bundles with specific properties over arithmetic curves, paralleling known results from algebraic curves.