03136nam 22006015 450 991014494190332120220406113542.03-540-48030-710.1007/b83848(CKB)1000000000233267(SSID)ssj0000324986(PQKBManifestationID)12098561(PQKBTitleCode)TC0000324986(PQKBWorkID)10320596(PQKB)10387521(DE-He213)978-3-540-48030-3(MiAaPQ)EBC6306531(MiAaPQ)EBC5591114(Au-PeEL)EBL5591114(OCoLC)1066185778(PPN)155187139(EXLCZ)99100000000023326720121227d2002 u| 0engurnn#008mamaatxtccrMonomialization of Morphisms from 3-Folds to Surfaces /by Steven D. Cutkosky1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (VIII, 240 p.)Lecture Notes in Mathematics,0075-8434 ;1786Bibliographic Level Mode of Issuance: Monograph3-540-43780-0 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.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.Lecture Notes in Mathematics,0075-8434 ;1786Geometry, AlgebraicAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Geometry, Algebraic.Algebraic Geometry.516.3514D06msc14E15mscCutkosky Steven Dauthttp://id.loc.gov/vocabulary/relators/aut725519MiAaPQMiAaPQMiAaPQBOOK9910144941903321Monomialization of morphisms from 3-folds to surfaces1415340UNINA