A SKELETON KEY TO ABHYANKAR'S PROOF OF EMBEDDED RESOLUTION OF CHARACTERISTIC P SURFACES

摘要

This paper analyzes and simplifies Abhyankar's proof of embedded resolution of surface singularities in positive characteristic. Abhyankar's proof is obtained by combining the results in the papers [2], [4], [5], [6] and the first two chapters of the book [7]. This proof is extremely influential, but because of its length and complexity, is not generally well known and understood. In this article, I have written a report on the proof, hoping to make the main ideas more generally known. I give complete proofs of the essential parts of the proof. Some lemmas, which are given complete self contained proofs in Abhyankar's work, are merely stated and cited in this paper. Some of these cited results can be proven directly without great difficulty. I have made substantial simplifications in the original proofs, but have made a point of not making simplications which eliminate an original and interesting idea which could possibly have application to resolution in higher dimension.