On the Jacobian locus in the Prym locus and geodesics

Abstract Let J g be the Jacobian locus and let P +1 Prym locus, in moduli space A of principally polarized abelian varieties dimension , for ≥ 7. We study extrinsic geometry ⊂ under inclusion provided by theory generalized introduced Beauville. More precisely, we address problem if certain geodesic curves, defined with respect to Siegel metric starting at a variety [ JC ] ∈ curve C M direction ζ T are locally contained . The result is that general answer negative, rank k such < Cliff − 3, where denotes Clifford index