Toward resolution of singularities over a field of positive characteristic (The idealistic filtration program). II: Basic invariants associated to the idealistic filtration and their properties

DOI10.2977/PRIMS/12zbMath1235.14017arXivmath/0612008OpenAlexW1985331442MaRDI QIDQ983318

Hiraku Kawanoue, Kenji Matsuki

Publication date: 22 July 2010

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612008

zbMATH Keywords

invariantspositive characteristicpower series expansionidealistic filtrationleading generator system

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Local theory in algebraic geometry (14B99)

Related Items (14)

Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties ⋮ Resolution of singularities of arithmetical threefolds ⋮ Techniques for the study of singularities with applications to resolution of 2-dimensional schemes ⋮ On the problem of resolution of singularities: its development and current status (from a myopic point of view of one researcher struggling with the problem) ⋮ Elimination with applications to singularities in positive characteristic ⋮ Partial local resolution by characteristic zero methods ⋮ Equimultiplicity, algebraic elimination, and blowing-up ⋮ Singularities in positive characteristic, stratification and simplification of the singular locus ⋮ Characterizing the increase of the residual order under blowup in positive characteristic ⋮ On the simplication of singularities by blowing up at equimultiple centers ⋮ Equivalence and resolution of singularities ⋮ On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for) ⋮ Resolution of Singularities: An Introduction ⋮ Multiplicity along points of a radicial covering of a regular variety

Uses Software

• LGS

Cites Work

• Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings
• Resolution of singularities of threefolds in positive characteristic. II
• Sur la théorie du contact maximal. (On the theory of maximal contact)

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