ar X iv : m at h / 00 12 25 1 v 2 [ m at h . A G ] 3 0 M ay 2 00 1 Euler Characteristics of Theta Divisors of Jacobians for Spectral Curves

ar X iv : 0 81 1 . 47 25 v 2 [ m at h . R A ] 1 2 M ay 2 00 9 On the deformation theory of structure constants for associative algebras

Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction. Deformations of associative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable systems are studied.

ar X iv : 0 70 7 . 46 02 v 3 [ m at h . A G ] 3 M ay 2 00 8 Geometry of the Theta Divisor of a compactified Jacobian

The object of this paper is the theta divisor of the compactified Jacobian of a nodal curve. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible stable curves is appended as an application.

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h - ph / 0 50 80 68 v 1 3 1 A ug 2 00 5 LAMÉ EQUATION , QUANTUM TOP AND ELLIPTIC BERNOULLI POLYNOMIALS

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.

ar X iv : 0 90 5 . 13 43 v 1 [ m at h . N T ] 8 M ay 2 00 9 A modular type formula for Euler infinite product ( 1 −

The main goal of this paper is to give a modular type representation for the infinite product (1−x)(1−xq)(1−xq)(1−xq) · · · . It is shown that this representation essentially contains the well-known modular formulae either for Dedekind’s eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions ...