Resumen de Theta divisors and the geometry of tautological model

Sonia Brivio

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