# Remarks on minimal rational curves on moduli spaces of stable bundles

@article{Liu2016RemarksOM,
title={Remarks on minimal rational curves on moduli spaces of stable bundles},
author={M. Liu},
journal={Comptes Rendus Mathematique},
year={2016},
volume={354},
pages={1013-1017}
}
• M. Liu
• Published 2016
• Mathematics
• Comptes Rendus Mathematique
Abstract Let C be a smooth projective curve of genus g ≥ 2 over an algebraically closed field of characteristic zero, and M be the moduli space of stable bundles of rank 2 and with fixed determinant L of degree d on the curve C . When g = 3 and d is even, we prove that, for any point [ W ] ∈ M , there is a minimal rational curve passing through [ W ] , which is not a Hecke curve. This complements a theorem of Xiaotao Sun.
1 Citations
Rational Curves on Moduli Spaces of Vector Bundles
• Mathematics
• 2020
We completely describe the components of expected dimension of the Hilbert Scheme of rational curves of fixed degree $k$ in the moduli space ${\rm SU}_{C}(r,L)$ of semistable vector bundles of rankExpand

#### References

SHOWING 1-10 OF 10 REFERENCES
Minimal rational curves on moduli spaces of stable bundles
Let C be a smooth projective curve of genus g ≥ 2 and L be a line bundle on C of degree d. Let M := UC(r,L) be the moduli space of stable vector bundles on C of rank r and with the fixed determinantExpand
Small rational curves on the moduli space of stable bundles
For a smooth projective curve C with genus g >= 2 and a degree 1 line bundle L on C, let M := SU_{C}(r;L) be the moduli space of stable vector bundles of rank r and with the fixed determinant L. InExpand
Elliptic curves in moduli space of stable bundles
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve onExpand
On Self-Intersection Number of a Section on a Ruled Surface
Let E be a non-singular projective curve of genus g ≥ 0, P the projective line and let F be the surface E× P . Then it is well known that a ruled surface F* which is birational to F is biregular to aExpand
Remarks on lines and minimal rational curves
• Mathematics
• 2008
We determine all of lines in the moduli space M of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.
Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques
• Mathematics
• 1989
Soient X une courbe algebrique projective lisse de genre g ≥ 2 sur ℂ, r, d des entiers, avec r ≥ 2. On note U(r,d) la variete de modules des fibres algebriques semi-stables sur X de rang r et deExpand