Stability of pullback of orbifold bundles

Soumyadip Das; Snehajit Misra

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arXiv · 2111.15652

Stability of pullback of orbifold bundles

Soumyadip Das·Snehajit Misra

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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.

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BibTeX RIS

Soumyadip Das, Snehajit Misra. 2021-11-30. Stability of pullback of orbifold bundles. https://arxiv.org/abs/2111.15652

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