Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Relative Frobenius of plane singularities

Author: D. Daigle
Journal: Trans. Amer. Math. Soc. 324 (1991), 777-791
MSC: Primary 14B05; Secondary 14H20
MathSciNet review: 1002919
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In view of the well-known conjecture concerning the classification of lines in the affine plane in characteristic $ p > 0$, it is desirable to understand how the characteristic pairs of an irreducible algebroid plane curve are affected by the relative Frobenius. This paper determines the relation between the characteristic sequences $ [x,y]$ and $ [x,{y^p}]$, where $ x$ and $ y$ are formal power series in one variable with coefficients in a field of characteristic $ p > 0$.

References [Enhancements On Off] (What's this?)

  • [1] S. Abhyankar and T. T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148-166. MR 0379502 (52:407)
  • [2] R. Ganong, Kodaira dimension of embeddings of the line in the plane, J. Math. Kyoto Univ. 25 (1985), 649-657. MR 810969 (87c:14013)
  • [3] T. T. Moh, On characteristic pairs of algebroid plane curves for characteristic $ p$, Bull. Math. Academia Sinica 1 (1973), 75-91. MR 0342517 (49:7263)
  • [4] -, On the classification problem of embedded lines in characteristic $ p$, Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata, 1987, pp. 267-279.
  • [5] M. Nagata, A theorem of Gutwirth, J. Math. Kyoto Univ. 11 (1971), 149-154. MR 0274448 (43:213)
  • [6] K. P. Russell, Hamburger-Noether expansions and approximate roots of polynomials, Manuscripta Math. 31 (1980), 25-95. MR 576491 (81g:14015)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14B05, 14H20

Retrieve articles in all journals with MSC: 14B05, 14H20

Additional Information

Keywords: Frobenius, characteristic pairs, embeddings of lines
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society