A remark on a theorem of Narasimhan and Ramanan

2024/11/24 by Jagadish Pine, Pine, Jagadish
Mathematics · #14C20 #14F05 #14H60 #Algebraic Geometry (math.AG) #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.15774

openalex publication_date 2024/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of S-equivalence classes of semistable rank 2 vector bundles over a curve X of genus 2 with trivial determinant is isomorphic to ℙ³. Our proof relies on a criterion by Bauer and Szemberg, which characterizes projective spaces among smooth Fano varieties using Seshadri constants.

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