1. Linear series on curves 1.1. Terminology and notation 1.2. Morphisms from linear series; Castelnuovo’s genus bound 1.3. Linear series from morphisms 1.4. Relation between linear series and morphisms 1.5. Hermitian invariants; Weierstrass semigroups I 2. Weierstrass point theory 2.1. Hasse derivatives 2.2. Order sequence; Ramification divisor 2.3. D-Weierstrass points 2.4. D-osculating spaces...

The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schrödinger equation with finite gap pote...

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...

We present the first examples of smooth elliptic Calabi-Yau threefolds with Mordell-Weil rank 10, highest currently known value. They are given by Schoen introduced Namikawa. explicitly compute Shioda homomorphism for generators group and their induced height pairing. There six isolated fibers Kodaira Type IV. Compactification F-theory on these gives an effective theory in dimensions which cont...

Let X denote an integral, projective Gorenstein curve over an algebraically closed field k. In the case when k is of characteristic zero, C. Widland and the second author ([22], [21], [13]) have defined Weierstrass points of a line bundle on X. In the first section, we extend this by defining Weierstrass points of linear systems in arbitrary characteristic. This definition may be viewed as a ge...

The Jordan canonical form (JCF) of a square matrix is a foundational tool in matrix analysis. If the matrix A is known exactly, symbolic computation of the JCF is possible though expensive. When the matrix contains parameters, exact computation requires either a potentially very expensive case discussion, significant expression swell or both. For this reason, no current computer algebra system ...

0932–0784 / 04 / 0100–0029 $ 06.00 c © 2004 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com Knyzazev and Goncharenko [8] used two transformations to obtain one-kink and two-kink solutions. Recently we developed a powerful Weierstrass elliptic function expansion method and its general form in terms of Weierstrass elliptic functions [11, 12], which was applied to see...