Minimal bundles and fine moduli spaces

We study coherent sheaves E on a smooth projective curve X which are minimal with respect to the property that h(0)(E circle times L) > 0 for all line bundles L of degree zero on X. We show that these sheaves define ample divisors D(E) on the Picard torus Pic(0)(X) (see Theorem 3.3). Next we classify all minimal sheaves of rank one (see Theorem 4.3) and two (see Theorem 4.4). As an application we show (see Proposition 5.5) that the moduli space parameterizing rank two bundles of odd degree can be obtained as a Quot scheme. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim