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02880nam a2200469 4500 |
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|a 9783540480303
|9 978-3-540-48030-3
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|a 10.1007/b83848
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|a Cutkosky, Steven D.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Monomialization of Morphisms from 3-Folds to Surfaces
|h [electronic resource] /
|c by Steven D. Cutkosky.
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|a 1st ed. 2002.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2002.
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|a VIII, 240 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1786
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|a 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.
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|a 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.
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|a Algebraic geometry.
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|a Algebraic Geometry.
|0 http://scigraph.springernature.com/things/product-market-codes/M11019
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662208861
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|i Printed edition:
|z 9783540437802
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1786
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|u https://doi.org/10.1007/b83848
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a ZDB-2-BAE
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|a Mathematics and Statistics (Springer-11649)
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