We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...

We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...

Abstract For even genus $$g=2i\ge 4$$ g=2i≥4 and the length $$g-1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">g-1 part...

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa’s discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projectivegeometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corresponding theta functions. We also present the reduction of the vectorial fundam...

Let $f\colon S'\longrightarrow S$ be a cyclic branched covering of smooth projective surfaces over $\mathbb{C}$ whose branch locus $\Delta\subset is ample divisor. Pick very complete linear system $|\mathcal{H}|$ on $S$, such that the polarized surface $(S, |\mathcal{H}|)$ not scroll nor has rational hyperplane sections. For general member $[C]\in|\mathcal{H}|$ consider $\mu_{n}$-equivariant is...

1 Introduction The Verlinde formula is a remarkable—and potentially very useful—new tool in the geometry of algebraic curves which is borrowed from conformal field theory. In the first instance it is a trigonometric expression which assigns a natural number N l (G, g) to data consisting of a semisimple algebraic group G, a nonnegative integer g and an auxiliary integer l ∈ Z. In physics N l (G,...

We introduce a new integrable hierarchy of nonlinear differential-difference equations which is subhierarchy the 2D Toda lattice defined by imposing constraint to Lax operators latter. The with can be regarded as discretization BKP hierarchy. construct its algebraic-geometrical solutions in terms Riemann and Prym theta-functions.