Tangent cones to generalised theta divisors and generic injectivity of the theta map

Abstract

Let be a Petri general curve of genus and a general stable vector bundle of rank and slope over with . For , we show how the bundle can be recovered from the tangent cone to the generalised theta divisor at . We use this to give a constructive proof and a sharpening of Brivio and Verra’s theorem that the theta map is generically injective for large values of .