Remarks on minimal rational curves on moduli spaces of stable bundles
Liu Min

TL;DR
This paper investigates minimal rational curves on the moduli space of stable rank 2 bundles with fixed determinant over a smooth projective curve, revealing the existence of non-Hecke minimal rational curves in specific cases.
Contribution
It demonstrates the existence of minimal rational curves that are not Hecke curves on the moduli space for genus 3 and even degree, extending previous results by Xiaotao Sun.
Findings
Existence of non-Hecke minimal rational curves for genus 3 and even degree
Minimal rational curves pass through any point in the moduli space
Complements prior work by Xiaotao Sun on Hecke curves
Abstract
Let M be the moduli space of stable bundles of rank 2 and with fixed determinant \mathcal{L} of degree d on a smooth projective curve C of genus g>= 2. When g=3 and d is even, we prove, for any point [W]\in M, there is a minimal rational curve passing through [W], which is not a Hecke curve. This complements a theorem of Xiaotao Sun.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Vietnamese History and Culture Studies · Advanced Algebra and Geometry
