The curve of "Prym canonical" gauss divisors on a Prym theta divisor

The Gauss linear system on the theta divisor of the Jacobian of a nonhypere lliptic curve has two striking properties: 1) the branch divisor of the Gauss map on the theta divisor is dual to the canonical model of the curve; 2) those divisors in the Gauss system parametrized by the canonical curve a re reducible. In contrast, Beauville and Debarre prove on a general Prym theta divisor of dimension greater than or equal to3 all Gauss divisors are irreducible and normal. One is led to ask whether properties 1) and 2) may characterize th e Gauss system of the theta divisor of a Jacobian. Since for a Prym theta d ivisor, the most distinguished curve in the Gauss system is the Prym canoni cal curve, the natural analog of the canonical curve for a Jacobian, in the present paper we analyze whether the analogs of properties 1) or 2) can ev er hold for the Prym canonical curve. We note that both those properties wo uld imply that the general Prym canonical Gauss divisor would be nonnormal. Then we find an explicit geometric model for the Prym canonical Gauss divi sors and prove the following results using Beauville's singularities criter ion for special subvarieties of Prym varieties: Theorem. For all smooth doubly covered nonhyperelliptic curves of genus g g reater than or equal to5, the general Prym canonical Gauss divisor is norma l and irreducible. Corollary. For all smooth doubly covered nonhyperelliptic curves of genus g greater than or equal to4, the Prym canonical curve is not dual to the bra nch divisor of the Gauss map.