Construction of the Moduli Space of Vector Bundles on an Orbifold Curve

2024/06/24 by Soumyadip Das, Das, Soumyadip, Souradeep Majumder +1
Engineering · Mathematics · #14A20 #14D20 #14D22 #14D23 (Primary) 14F06 #14G17 (Secondary) #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2406.16337

openalex publication_date 2024/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of any characteristic, and let (X,P) be an orbifold curve over k. We construct the moduli space M_(X,P)^ss(n, Δ) of P-semistable bundles on (X,P) of rank n and determinant Δ. In the characteristic zero case, this result is well known and follows from GIT techniques. Our construction follows a different approach inspired by a GIT-free construction of Faltings. We show that when the moduli space is non-empty, it is a finite disjoint union of irreducible projective varieties.

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