# Remarks on lines and minimal rational curves

@article{Mok2008RemarksOL, title={Remarks on lines and minimal rational curves}, author={Ngaiming Mok and Xiaotao Sun}, journal={Science in China Series A: Mathematics}, year={2008}, volume={52}, pages={617-630} }

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.

#### 12 Citations

Remarks on minimal rational curves on moduli spaces of stable bundles

- Mathematics
- 2015

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… Expand

Small rational curves on the moduli space of stable bundles

- Mathematics
- 2011

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. In… Expand

Remarks on minimal rational curves on moduli spaces of stable bundles

- Mathematics
- 2016

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… Expand

Elliptic Curves in Moduli Space of Stable Bundles

- 2011

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 ≥ 2. When C is generic, we show that any elliptic curve on M has degree… Expand

LOCI OF RATIONAL CURVES OF SMALL DEGREE ON THE MODULI SPACE OF VECTOR BUNDLES

- Mathematics
- 2011

For a smooth algebraic curve C of genus g 4, let (r, d) be the moduli space of semistable bundles of rank r 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that (r, d) is a… Expand

Elliptic Curves in Moduli Space of Stable Bundles of Rank 3

- Mathematics
- 2012

Let $M$ be the moduli space of rank 3 stable bundles with fixed determinant of degree 1 on a smooth projective curve of genus $g\geq 2$. When $C$ is generic, we show that any essential elliptic curve… Expand

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 rank… Expand

Elliptic curves in moduli space of stable bundles

- Mathematics
- 2010

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 on… Expand

On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve

- Mathematics
- 2012

Let M(n, ξ) be the moduli space of stable vector bundles of rank n ≥ 3 and fixed determinant ξ over a complex smooth projective algebraic curve X of genus g ≥ 4. We use the gonality of the curve and… Expand

An inexact smoothing method for the monotone complementarity problem over symmetric cones

- Mathematics, Computer Science
- Optim. Methods Softw.
- 2012

It is shown that any accumulation point of generated sequence is a solution of SCCP and it is proved that the proposed algorithm is locally superlinearly/quadratically convergent under suitable conditions. Expand

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