# Minimal rational curves on moduli spaces of stable bundles

@article{Sun2003MinimalRC,
title={Minimal rational curves on moduli spaces of stable bundles},
author={Xiaotao Sun},
journal={Mathematische Annalen},
year={2003},
volume={331},
pages={925-937}
}
• Xiaotao Sun
• Published 2003
• Mathematics
• Mathematische Annalen
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 L. Assume that (r, d) = 1, then M is a smooth projective Fano variety with Picard number 1. For any projective curve on M , we can define its degree with respect to the ample anti-canonical line bundle −KM . The first result of this paper determines all rational curves of minimal degree passing… Expand
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#### References

SHOWING 1-10 OF 12 REFERENCES
Degenerations of the moduli spaces of vector bundles on curves I
• Mathematics, Chemistry
• 1995
LetY be a smooth projective curve degenerating to a reducible curveX with two components meeting transversally at one point. We show that the moduli space of vector bundles of rank two and oddExpand
Hecke curves and Hitchin discriminant
• Mathematics
• 2003
Abstract Let C be a smooth projective curve of genus g ⩾ 4 over the complex numbers and SU C s ( r , d ) be the moduli space of stable vector bundles of rank r with a fixed determinant of degree d.Expand
Moduli of high rank vector bundles over surfaces
• Mathematics
• 1994
The purpose of this work is to apply the degeneration theory developed in [GL] to study the moduli space of stable vector bundles of arbitrary rank on any smooth algebraic surface (over C). We willExpand
The automorphism group of the moduli space of semi stable vector bundles
• Mathematics
• 1993
Let ${\cal S}{\cal U}(r, L_0)$ denote the moduli space of semi stable vector bundles of rank $r$ and fixed determinant $L_0$ of degree $d$ on a smooth curve $C$ of genus $g \geq 3$. In this paper weExpand
Rational curves on algebraic varieties
• J. Kollár
• Mathematics, Computer Science
• Ergebnisse der Mathematik und ihrer Grenzgebiete
• 1996
It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane. Expand
The automorphism group of the moduli space of semi - stable bundles
• Math . Ann .
• 1995
Geometry of Hecke cycles I., in C. P. Ramanujama tribute
• Geometry of Hecke cycles I., in C. P. Ramanujama tribute
• 1978