# 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} }

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.

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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

#### References

SHOWING 1-10 OF 10 REFERENCES

Minimal rational curves on moduli spaces of stable bundles

- Mathematics
- 2003

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 determinant… 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

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 Self-Intersection Number of a Section on a Ruled Surface

- Mathematics
- 1970

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 a… Expand

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 de… Expand