On the Abhyankar-Moh inequality

Roland D. Barrolleta,

Evelia R Garcia Barroso,

Arkadiusz Ploski


In their fundamental paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality which can be stated in terms of the semigroup associated with the branch at in nity of a plane algebraic curve. In this note we study the semigroups of integers satisfying the Abhyankar-Moh inequality and describe such semigroups with the maximum conductor.

Słowa kluczowe: Branches at in nity, semigroups, sequences of divisors, Abhyankar-Moh inequality

1. Abhyankar S. S., Moh T. T., Embeddings of the line in the plane, J. Reine Angew. Math., 276 (1975), 148–166.

2. Angermu¨ller G., Die Wertehalbgruppe einer ebener irreduziblen algebroiden Kurve, Math. Z., 153(3) (1977), 267–282.

3. Barrolleta R., Semigrupos en teor´ıa de singularidades: aplicaciones a los c´odigos, Memoria fin de M´aster, Universidad de La Laguna, Tenerife (2013).

4. Garcıa  Barroso E. R., Płoski  A.,  An  approach to  plane algebroid branches,  Revista Matem´atica Complutense (2014). doi: 10.1007/s13163-014-0155-5. First published online: July 29, 2014.

5. Gwoździewicz J., Płoski  A., On the approximate roots of polynomials, Ann. Polon. Math., 60(3) (1995), 199–210.

6. Hefez A.,  Irreducible  plane curve singularities,  Real and complex singularities, 1–120, Lecture Notes in Pure and Appl. Math., 232, Dekker, New York, 2003.

7. Sathaye A., Stenerson, J., Plane polynomial curves, Algebraic geometry and its applications (West Lafayette, IN, 1990), 121–142, Springer, New York, 1994.

8. Seidenberg A., Elements of the theory of algebraic curves, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1968, viii+216 pp.

Czasopismo ukazuje się w sposób ciągły on-line.
Pierwotną formą czasopisma jest wersja elektroniczna.