Monomialization of Morphisms from 3 Folds to Surfaces
By Steven Dale Cutkosky. 2000
56 citations recorded by the source corpus.
1. Introduction.- 2. Local Monomialization.- 3. Monomialization of Morphisms in Low Dimensions.- 4. An Overview of the Proof of Monomialization of Morphisms from 3 Folds to Surfaces.- 5. Notations.- 6. The Invariant v.- 7. The Invariant v under Quadratic Transforms.- 8. Permissible Monoidal Transforms Centered at Curves.- 9. Power Series in 2 Variables.- 10. Ar(X).- 11.Reduction of v in a Special Case.- 12. Reduction of v in a Second Special Case.- 13. Resolution 1.- 14. Resolution 2.- 15. Resolution 3.- 16. Resolution 4.- 17. Proof of the main Theorem.- 18. Monomialization.- 19. Toroidalization.- 20. Glossary of Notations and definitions.- References.
Subfields: Organic Chemistry, Physical and Theoretical Chemistry
View Paper: https://www.semanticscholar.org/paper/f68819609340ee8990be3b1092923b99ecae07aa
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- Steven Dale Cutkosky
- Shreeram S. Abhyankar
- Chi Li
- Kiumars Kaveh
- Franz-Viktor Kuhlmann
- Christopher D. Hacon
Citations in the corpus
- Resolution of Singularities (2004, background): “Then the Puiseux series (2.5) of Section 2.1 determines an inclusion (2.7) R = K[[x, y]]/(f(x, y)) → K[[t]]”
- Resolution of singularities for 3-folds in positive characteristic (2006, background): “ a drop in ct. The problem with order going up under resolution also occurs in resolution of vector fields (Seidenberg [Se], Cano [Ca] and Panazzolo [Pa]) and in monomialization of morphisms (Cutkosky [C1], [C3]; and Cutkosky and Piltant [CP]). In the case of dimension two (as in the case of resoluti”