Semigroups corresponding to algebroid branches in the plane
| Autor: | H. Bresinsky |
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| Rok vydání: | 1972 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 32:381-384 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1972-0291171-1 |
| Popis: | The symmetric semigroups of nonnegative integers and their generators, corresponding to algebroid branches of the plane, are determined. Let a be an algebroid branch of a plane curve with coefficients in an algebraically closed field with characteristic 0. Although the semigroup S(a) of a is symmetric, not all symmetric semigroups correspond to branches [1]. Subsequently the nonredundant generators of S(a) are found from which follow necessary and sufficient conditions for a nonredundant set of positive integers to generate the semigroup of a branch a. A method for obtaining the generators from the power series is given. The definitions for infinitely near points Pi, multiplicity sequence, proximity structure, satellite cluster and multiplicity matrix are given in [3]. By the restriction of a point P3 we mean the number of points Pj is proximate to, and the leading points are the points which have successors with increased restriction. Defining the order of a divisor D on a, o(D, a), in the usual way, let v(Pj, a)=min(o(D, a)), where a passes thru P3 and D is a divisor of Pi. LEMMA 1. If a has satellite clusters Sl, , Sn and a* is obtainedfrom a by deleting Sn, then v(Pj, a)=cv(Pj, a*), O |
| Databáze: | OpenAIRE |
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