Weak toroidalization over non-closed fields

DOI10.1007/s00229-013-0610-5zbMath1279.14020arXiv1010.6171OpenAlexW1966804110MaRDI QIDQ361834

Dan Abramovich, Kalle Karu, Jan Denef

Publication date: 19 August 2013

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.6171

zbMATH Keywords

resolution of singularitiesgroup actiontoroidal embeddingalterationmodificationsemistable family of curvestoroidal morphism

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Families, moduli of curves (algebraic) (14H10) Local structure of morphisms in algebraic geometry: étale, flat, etc. (14B25)

Related Items

Toroidalization of locally toroidal morphisms from \(n\)-folds to 3-folds, Some aspects of rational points and rational curves, Existence of canonical models for Kawamata log terminal pairs, Monomialization of a quasianalytic morphism, Principalization of ideals on toroidal orbifolds, Local monomialization of analytic maps, Proof of a conjecture of Colliot-Thélène and a Diophantine excision theorem, The tight approximation property, Monomialization of morphisms and p-adic quantifier elimination, Toroidalization of locally toroidal morphisms

Cites Work

• Toroidal embeddings. I
• Good points and constructive resolution of singularities
• Families of curves and alterations
• Smoothness, semi-stability and alterations
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Weak semistable reduction in characteristic 0
• The tame fundamental groups of a formal neighbourhood of a divisor with normal crossings on a scheme
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• Local monomialization of transcendental extensions.
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Geometric proofs of theorems of Ax-Kochen and Eršov
• Introduction to Toric Varieties. (AM-131)
• Toric singularities: Log-blow-ups and global resolutions
• Lectures on Resolution of Singularities (AM-166)
• Logarithmic structures of Fontaine-Illusie. II
• Torification and factorization of birational maps
• Smoothness, Semistability, and Toroidal Geometry
• Toroidalization of dominant morphisms of 3-folds
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