Stability of pullback of orbifold bundles

Abstract

In this article, we study the behavior of the stability of pullback of a vector bundle under a finite morphism from a (not necessarily smooth) stacky curve to an orbifold curve. We establish a categorical equivalence between proper formal orbifold curves and proper orbifold curves in the sense of Deligne-Mumford stacks. Using this identification, we define the notion of slope $P$-(semi)stability of vector bundles on proper formal orbifold curves $(X,P)$. We establish some equivalent conditions for a stacky genuinely ramified morphism, analogous to the case of curves. Finally, we show that for a cover of an orbifold curve arising as a cartesian pullback via a genuinely ramified morphism of smooth projective connected curves, the orbifold slope stability is preserved under the pullback.

The second author requested to withdraw from the project. An updated version with complete results on this problem will be posted under the authorship of the first author

References in corpus (1)

• Parabolic bundles in positive characteristic