Summary
In my 1967 paper with almost the same title which appeared in volume 89 of the American Journal of Mathematics, I proved the invariance of the characteristic terms in the fractional power series expansion of a branch of an algebraic plane curve over fields of characteristic zero. Now I extend the results by a more generous interpretation of the characteristic terms, and by relaxing the characteristic zero hypothesis.
Mathematics Subject Classification (2000) Primary 14H20; Secondary 13F30
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Acknowledgments
On the algebraic side, my thanks are to Pierrette Cassou-Noguès, Bill Heinzer, Giulio Peruginelli, Avinash Sathaye, and Dave Shannon for numerous useful discussions. On the topological side, my thanks are to Dung Trang Le, Walter Neumann, Stepan Orevkov, and Claude Weber for many stimulating discussions. But above all, several private lectures which were given to me by Enrique Artal-Bartolo and Arnaud Bodin in Lille in July 2008 have been most helpful for clarifying the theory of dicritical divisors.
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Fondly dedicated to the 104th birthday of my father Professor S.K. Abhyankar who was born on 4/4/1904 Also dedicated to the memory of Professor Alladi Ramakrishnan in great admiration
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Abhyankar, S.S. (2010). Inversion and Invariance of Characteristic Terms: Part I. In: Alladi, K., Klauder, J., Rao, C. (eds) The Legacy of Alladi Ramakrishnan in the Mathematical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6263-8_8
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