Theta divisors and the geometry of tautological model

Let E be a stable vector bundle of rank r and slope 2g - 1 on a smooth irreducible complex projective curve C of genus g >= 3. In this paper we show a relation between theta divisor and the geometry of the tautological model of E. In particular, we prove that for , if C is a Petri curve and E is general in its moduli space then defines an irreducible component of the variety parametrizing -linear spaces which are g-secant to the tautological model . Conversely, for a stable, -very ample vector bundle E, the existence of an irreducible non special component of dimension of the above variety implies that E admits theta divisor.