Loci of rational curves of small degree on the moduli space of vector bundles
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 377-386
https://doi.org/10.4134/BKMS.2011.48.2.377
Printed March 1, 2011
Insong Choe
Konkuk University
Abstract : For a smooth algebraic curve $C$ of genus $g\ge 4$, let $SU_C(r,d)$ be the moduli space of semistable bundles of rank $r \ge 2$ over $C$ with fixed determinant of degree $d$. When $(r,d)=1$, it is known that $SU_C(r,d)$ is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\ge r$ with respect to the ample generator of $Pic(SU_C(r,d))$. In this paper, we study the locus swept out by the rational curves on $SU_C(r,d)$ of degree $
Keywords : rational curves, moduli of vector bundles over a curve, scroll, Torelli theorem
MSC numbers : 14C34, 14H60
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