Monomialization of Morphisms from 3-Folds to Surfaces

Steven D. Cutkosky (Autor)

Buch | Softcover

VIII, 240 Seiten

2002 | 2002
Springer Berlin (Verlag)
978-3-540-43780-2 (ISBN)

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A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S.
The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.

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.

Erscheint lt. Verlag	6.8.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 240 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	382 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebraic Varieties • algebraic variety • Algebraische Geometrie • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • HC/Mathematik/Geometrie • Monomialization • Morphische Felder • Morphism • Resolution of Singularities
ISBN-10	3-540-43780-0 / 3540437800
ISBN-13	978-3-540-43780-2 / 9783540437802
Zustand	Neuware