Monomial resolutions of morphisms of algebraic surfaces

DOI10.1080/00927870008827198zbMath1003.14004arXivmath/9910076OpenAlexW1984595969MaRDI QIDQ2707901

Steven Dale Cutkosky, Olivier Piltant

Publication date: 27 January 2003

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9910076

zbMATH Keywords

monomializationfield extension of two-dimensional function fields

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Rational and birational maps (14E05) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (10)

Monomialization of strongly prepared morphisms from nonsingular \(n\)-folds to surfaces ⋮ Toroidalization of locally toroidal morphisms from \(N\)-folds to surfaces ⋮ Ramification of valuations ⋮ A simpler proof of toroidalization of morphisms from 3-folds to surfaces ⋮ Torification and factorization of birational maps ⋮ On the Jung method in positive characteristic. ⋮ Toroidal varieties and the weak factorization theorem ⋮ Local monomialization of transcendental extensions. ⋮ Toroidalization of locally toroidal morphisms ⋮ A principalization algorithm for locally monomial ideal sheaves on 3-folds with an application to toroidalization

Cites Work

• Toroidal embeddings. I
• Local uniformization on algebraic surfaces over ground fields of characteristic \(p\neq 0\)
• Desingularization of two-dimensional schemes
• Weak semistable reduction in characteristic 0
• Rational singularities, with applications to algebraic surfaces and unique factorization
• The tame fundamental groups of a formal neighbourhood of a divisor with normal crossings on a scheme
• Local uniformization on algebraic varieties
• Valuations in Function Fields of Surfaces
• Simultaneous Resolution for Algebraic Surfaces
• On the Valuations Centered in a Local Domain
• Tame Coverings and Fundamental Groups of Algebraic Varieties: Part I: Branch Loci with Normal Crossings; Applications: Theorems of Zariski and Picard

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