The degree of the Gauss map for a general Prym theta-divisor (Q2710515)

Let \(X\) be an abelian variety of dimension \(d\) admitting a principal polarization given by a theta divisor \(\theta\). Let \(\gamma: \theta\to \mathbb{P}_{d-1}\) denote its Gauss map. The degree of \(\gamma\) is finite unless \(X\) is a product and varies according to the singularities of \(\theta\). In the case of Jacobians \(\gamma\) is closely related to the canonical curve, and this is the only case where it is completely understood. The focus of the paper under review is to study the Gauss map for general Prym varieties. As a main result it is shown that for a general Prym variety of dimension \(g-1\geq 2\) the degree of the Gauss map is \(D(g)+2^{g-3}\), where \(D(g)\) is the degree of the variety of all quadrics of rank \(\geq 3\) in \(\mathbb{P}_{g-1}\).