We construct pointed Prym–Brill–Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with prescribed minimal vanishing at fixed point. realize them as degeneracy loci in type D and deduce their classes case expected dimension. Thus, we determine Prym–Petri map prove version the theorem implying that dimension holds general case. These results ...

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The solutions are completely classified by the structure of the zeros of the ...

We use Heegaard decompositions and the theta divisor on a Riemann-ian surface to define a three-manifold invariant for rational homology three-spheres. This invariant is defined on the set of Spin c structures θ : Spin c (Y) −→ Q. In the first part of the paper, we give the definition of the invariant (which builds on the theory developed in [18]). In the second part, we establish a relationshi...

Let Mr denote the moduli space of semi-stable rank-r vector bundles with trivial determinant over a smooth projective curve C of genus g. In this paper we study the base locus Br ⊂ Mr of the linear system of the determinant line bundle L over Mr, i.e., the set of semi-stable rank-r vector bundles without theta divisor. We construct base points in Bg+2 over any curve C, and base points in B4 ove...

The classical Poincar\'e formula relates the rational homology classes of tautological cycles on a Jacobian to powers class Riemann theta divisor. We prove tropical analogue this formula. Along way, we several foundational results about real tori with integral structures (and, therefore, abelian varieties). For example, version Appell-Humbert theorem. also study various notions equivalences bet...

We present a Prym construction which associates abelian varieties to vertex-transitive strongly regular graphs. As an application we construct Prym-Tyurin varieties of arbitrary exponent ≥ 3, generalizing a result by Lange, Recillas and Rochas.