LEADER 03136nam 22006015 450 001 9910144941903321 005 20220406113542.0 010 $a3-540-48030-7 024 7 $a10.1007/b83848 035 $a(CKB)1000000000233267 035 $a(SSID)ssj0000324986 035 $a(PQKBManifestationID)12098561 035 $a(PQKBTitleCode)TC0000324986 035 $a(PQKBWorkID)10320596 035 $a(PQKB)10387521 035 $a(DE-He213)978-3-540-48030-3 035 $a(MiAaPQ)EBC6306531 035 $a(MiAaPQ)EBC5591114 035 $a(Au-PeEL)EBL5591114 035 $a(OCoLC)1066185778 035 $a(PPN)155187139 035 $a(EXLCZ)991000000000233267 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMonomialization of Morphisms from 3-Folds to Surfaces /$fby Steven D. Cutkosky 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (VIII, 240 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1786 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-43780-0 327 $a1. 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. 330 $aA morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1786 606 $aGeometry, Algebraic 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aGeometry, Algebraic. 615 14$aAlgebraic Geometry. 676 $a516.35 686 $a14D06$2msc 686 $a14E15$2msc 700 $aCutkosky$b Steven D$4aut$4http://id.loc.gov/vocabulary/relators/aut$0725519 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144941903321 996 $aMonomialization of morphisms from 3-folds to surfaces$91415340 997 $aUNINA