Projectivity of good moduli spaces of vector bundles on stacky curves

2024/07/05 by Chiara Damiolini, Damiolini, Chiara, Victoria Hoskins +5
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2407.04412

openalex publication_date 2024/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli spaces of stacks to show that the moduli stack of semistable vector bundles on a stacky curve has a proper good moduli space. We moduli-theoretically prove that a natural determinantal line bundle on this moduli space is ample, thus proving this moduli space is projective. Our methods give effective bounds for when a power of this line bundle is basepoint-free. As a special case, we obtain new and effective constructions of moduli spaces of parabolic bundles.

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