New Component of the Moduli Space M(2;0,3) of Stable Vector Bundles on the Double Space P3 of Index Two

Abstract

We study the moduli scheme M(2;0,n) of rank-2 stable vector bundles with Chern classes c1=0, c2=n, on the Fano threefold X – the double space P3 of index two. New component of this scheme is produced via the Serre construction using certain families of curves on X. In particular, we show that the Abel–Jacobi map Φ: H→J(X) of any irreducible component H of the Hilbert scheme of X containing smooth elliptic quintics on X into the intermediate Jacobian J(X) of X factors by Stein through the quasi-finite (probably birational) map g: M→Θ of (an open part of) a component M of the scheme M(2;0,3) to a translate Θ of the theta-divisor of J(X).