Buser-Sarnak invariants of Prym varieties (Q376678)

The Buser-Sarnak invariant of a principally polarized complex abelian variety is roughly speaking the minimal length of a non-zero period. \textit{P. Buser} and \textit{P. Sarnak} showed in [Invent. Math. 117, No. 1, 27--56 (1994; Zbl 0814.14033)] that in the case of a Jacobian the invariant is particularly small. \textit{R. Lazarsfeld} gave in [Math. Res. Lett. 3, No. 4, 439--447 (1996; Zbl 0890.14025)] a weaker upper bound in the algebraic case using an interpretation of the invariant in terms of Seshadri constants. \textit{T. Bauer} generalized in [Math. Ann. 312, No. 4, 607--623 (1998; Zbl 0933.14025)] this upper bound to the case of Prym varieties.NEWLINENEWLINE The present paper gives an analogue of the better original Buser-Sarnak estimate for Prym varieties using differential geometric methods. As an application examples of period matrices in high dimension are given which do not come from Prym varieties.