On the Computation of Weierstrass Gap Sequences
نویسنده
چکیده
In this paper, we develop a technique to compute the Weierstrass Gap Sequence at a given point, no matter if simple or singular, on a plane curve, with respect to any linear system V ⊆ H(C,OC (n)). This technique can be useful to construct examples of curves with Weierstrass points of given weight, or to look for conditions for a sequence to be a Weierstrass Gap Sequence. We use this technique to compute the Weierstrass Gap Sequence at a point of particular curves and of families of curves.
منابع مشابه
Gap Sequences and Moduli in Genus 4
Let X denote a compact Riemann surface of genus g > 1. At each point P~X, there is a sequence of g integers, l=71(P)<72(P)<. . .<Tg(P)<2g , called the Weierstrass gap sequence at P. A positive integer ~/is a Weierstrass gap at P if there exists a holomorphic differential on X with a zero of order 7 1 at P. A positive integer which is not a gap at P is called a nongap at P. The point P is called...
متن کاملComputation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
The Sadhana index (Sd) is a newly introduced cyclic index. Efficient formulae for calculating the Sd (Sadhana) index of linear phenylenes are given and a simple relation is established between the Sd index of phenylenes and of the corresponding hexagonal sequences.
متن کاملGeneralized Wronskians and Weierstrass Weights
Given a point P on a smooth projective curve C of genus g, one can determine the Weierstrass weight of that point by looking at a certain Wronskian. In practice, this computation is difficult to do for large genus. We introduce a natural generalization of the Wronskian matrix, which depends on a sequence of integers s = m0, . . . ,mg−1 and show that the determinant of our matrix is nonzero at P...
متن کاملWeierstrass Pairs and Minimum Distance of Goppa Codes
We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of particular codes defined using a linear combination o...
متن کاملDetermining the order of minimal realization of descriptor systems without use of the Weierstrass canonical form
A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present ...
متن کامل