Minimal Rational Curves in Moduli Spaces of Stable Bundles
نویسندگان
چکیده
Let C be a smooth projective curve of genus g ≥ 2 and L be a line bundle on C of degree d. Assume that r ≥ 2 is an integer coprime with 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. It is well-known that M is a smooth projective Fano variety with Picard number 1. For any projective curve in M , we can define its degree with respect to the ample anti-canonical line bundle −KM . A natural question raised by Jun-Muk Hwang (see Question 1 in [Hw]) is to determine all rational curves of minimal degree passing through a generic point of M . In this short note, we prove the following theorem
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