English

Real line subbundles of real bundles on curves

Algebraic Geometry 2026-03-16 v1 Differential Geometry

Abstract

For a stable real bundle EE of rank 22 and degree 11 on a real genus 22 curve, we describe the action of the real structure of the curve on the set of 44 maximal line subbundles of degree 00 of EE. This describes the Galois action on the set of lines through a real point in the moduli space of such bundles, and is a real algebraic extension of classical work of Newstead. Our proof is an application of techniques of Atiyah from the 1950's. We prove also results on real line subbundles in higher genus using work of Lange-Narasimhan.

Keywords

Cite

@article{arxiv.2603.12569,
  title  = {Real line subbundles of real bundles on curves},
  author = {Daniel A. Santiago Alvarez},
  journal= {arXiv preprint arXiv:2603.12569},
  year   = {2026}
}