Book Review: Resolution of curve and surface singularities in characteristic zero
نویسندگان
چکیده
منابع مشابه
Strong resolution of singularities in characteristic zero
Hironaka's spectacular proof of resolution of singularities is built on a multiple and intricate induction argument. It is so involved that only few people could really understand it. The constructive proofs given later by Villamayor, Bierstone-Milman and Encinas-Villamayor presented important steps towards a better understanding of the reasoning. They describe an algorithmic procedure for reso...
متن کاملWhy the characteristic zero proof of resolution of singularities fails in positive characteristic
This is – for the time being – the last of a series of papers of the author on resolution of singularities. This series started with a collection of obstacles which make resolution in arbitrary dimension and characteristic difficult [Ha 1]. It was followed by a comprehensive study of Hironaka’s proposal for surface resolution in positive characteristic [Ha 2], in order to see whether this appro...
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We propose alternative invariants for the inductive proof of the resolution of surfaces in positive characteristic by a sequence of blowups. The invariants are more systematic than the existing ones, and yield a quite transparent reasoning. This may facilitate the study of the still unsolved case of the embedded resolution of threefolds in positive characteristic. CONTENTS
متن کاملOn the Problem of Resolution of Singularities in Positive Characteristic
Introduction. The embedded resolution of singular algebraic varieties of dimension > 3 defined over fields of characteristic p > 0 is still an open problem. The inductive argument which works in characteristic zero fails for positive characteristic. The main obstruction is the failure of maximal contact, which, in turn, manifests in the occurence of wild singularities and kangaroo points at cer...
متن کاملNew Ideas for Resolution of Singularities in Arbitrary Characteristic
I have succeeded in showing that any two-dimensional hypersur-face singularities of germs of varieties in any characteristic can be resolved by iterated monoidal transformations with centers in smooth subvarieties. The new proof for the two-dimensional case depends on new ideas. Ideas are essentially diierent from Abhyankar's one in 1] and Lipman's one in 7]. It seems to be possible to generali...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2006
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-06-01105-0