A TORELLI THEOREM FOR SPECIAL DIVISOR VARIETIES X ASSOCIATED TO DOUBLY COVERED CURVES ${\tilde C}/C$

Let Ci, i=1,2, be two smooth non-hyperelliptic curves over the complex numbers of genus g≥ 3, and [Formula: see text] connected étale double covers, such that the theta divisors Ξi of the associated Prym varieties (pi, Ξi) are non singular in codimension ≤ 3. If [Formula: see text] are the norm maps, then Ξi is isomorphic to {[Formula: see text] and h0 (L) is even and positive}. Then the Abel maps define generic ℙ1 bundles Xi→Ξi, where Xi is the special divisor variety [Formula: see text] and [Formula: see text] even}. We prove, under the hypotheses above, that biregular isomorphism of the special divisor varieties X1≅ X2 implies isomorphism of the double covers [Formula: see text].