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arXiv · 1401.0556

Stability of vector bundles on curves and degenerations

Brian Osserman
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Abstract

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of polarization. We introduce and explore the basic properties of this alternate notion of (semi)stability. In a complementary direction, we record a proof of the existence of semistable extensions of vector bundles in suitable degenerations.

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Brian Osserman. 2014-01-02. Stability of vector bundles on curves and degenerations. https://doi.org/10.4153/cmb-2016-008-2

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