Publication: On pythagorean real irreducible algebroid curves
Loading...
Official URL
Full text at PDC
Publication Date
1984
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Rocky Mountain Mathematics Consortium
Citations
Exportar
Abstract
In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two theorems involving the value-semigroup. Then we apply them to solve the cases of: (a) Gorenstein curves, (b) planar curves, (c) monomial curves, and (d) curves of multiplicity <= 5. Finally, two conjectures are stated.
Description
UCM subjects
Unesco subjects
Keywords
Citation
A. Campillo, Algebroid curves in positive characteristic. Lecture Notes in Mathematics 813, Springer-Verlag, New York, 1980
S. Ebey, The classification of singular points of algebraic curves, Trans. A.M.S. 118 (1965), 454-471
E. Kunz, The value-semigroup of a one-dimensional Gorenstein rign. Proc. A.M.S. 25 (1970), 748-751
J. Lipman, Stable ideals and Arf rings, Amer. J. Math. 93 (1971), 649-685
J. M. Ruiz, Ph. D. Dissertation, Univ. Complutense de Madrid, 1982
J. M. Ruiz, On Pythagorean real curve germs, preprint, 1983