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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 smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree r with respect to the ampl generator of Pic((r, d)). In this paper, we study the locus swept out by the rational curves on (r, d) of degree (r, d).

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