Prym varieties provide a correspondence between the moduli spaces of curves and abelian varieties Mg and Ag−1, via the Prym map Pg : Rg → Ag−1 from the moduli space Rg parameterizing pairs [C, η], where [C] ∈ Mg is a smooth curve and η ∈ Pic(C)[2] is a torsion point of order 2. When g ≤ 6 the Prym map is dominant and Rg can be used directly to determine the birational type ofAg−1. It is known t...

The periods of Prym differentials can be used to prove the invariance of Picard bundles on Jacobian varieties. Let S be a compact Riemann surface of genus g with universal covering surface 77 with the deck transformation group D. For any homomorphism X: D -> C* = C {0} into the group of complex units, a (meromorphic) Prym differential on S1 with multipliers A1 is a meromorphic differential w on...

We show that the non-Archimedean skeleton of Prym variety associated to an unramified double cover algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) cover. This confirms conjecture by Jensen and first author. prove new upper bound on dimension Prym-Brill-Noether locus for generic covers curves with fixed even gonality base. Our methods also give proof...

By the theory of Eisenstein series, generating functions various divisor arise as modular forms. It is natural to ask whether further systematically in mock We establish, using method Zagier and Zwegers on holomorphic projection, that this indeed case for certain (twisted) “small divisors” summatory [Formula: see text]. More precisely, terms weight 2 quasimodular series text] a generic Shimura ...

We investigate a family of correspondences associated tó etale coverings of degree 3 of hyperelliptic curves. They lead to Prym-Tyurin varieties of exponent 3. We identify these varieties and derive some consequences.

In the theory of elliptic functions, there are two kinds of determinantal formulae of Frobenius-Stickelberger [6] and of Kiepert [7], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through an determinantal expression. These formulae were naturally generalized to hyperelliptic functions by the papers [11], [12], and [13]. Avoiding generality, we restrict the story...