On the essential dimension of symplectic vector bundles over curves

2024/12/06 by Chowdhury, Ajneet Dhillon Sayantan Roy, Dhillon, Ajneet, Chowdhury, Sayantan Roy
Mathematics · #14D23 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2412.05375

openalex publication_date 2024/12/06 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth geometrically connected projective curve of genus at least 2 over a field of characteristic zero. We compute the essential dimension of the moduli stack of symplectic bundles over X. Unlike the case of vector bundles, we are able to precisely compute the essential dimension as the generic gerbe of the moduli stack has period 2 over it's moduli space.

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