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dc.contributor.advisorCutkosky, Steven Daleen
dc.contributor.authorHanumanthu, Krishna Chaithanya, 1981-en_US
dc.date.issued2008eng
dc.date.submitted2008 Springen
dc.descriptionThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.en_US
dc.descriptionTitle from title screen of research.pdf file (viewed on June 8, 2009)en_US
dc.descriptionVita.en_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionThesis (Ph. D.) University of Missouri-Columbia 2008.en_US
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.en_US
dc.description.abstractLet X and Y be nonsingular varieties over an algebraically closed field [kappa] of characteristic zero. A toroidal structure on X is a simple normal crossing divisor DX on X. Suppose that DX and DY are toroidal structures on X and Y respectively. A dominant morphism [function] : X [arrow] Y is toroidal (with respect to the toroidal structures DX and DY ) if for all closed points [rho] 2 X, [function] is isomorphic to a toric morphism of toric varieties specified by the toric charts at [rho] and [function] [rho]. A dominant morphism [function] : X [arrow] Y of nonsingular varieties is toroidalizable if there exist sequences of blow ups with nonsingular centers [pi] : Y₁ [arrow] Y and [pi]₁ : X₁ [arrow] X so that the induced map [function]₁ : X1 [arrow] Y1 is toroidal. Let [function] : X [arrow] Y be a dominant morphism. Suppose that there exist finite open covers (Ui) and (Vi) of X and Y respectively such that [function] (Ui) [arrow] Vi and the restricted morphisms [function] : (Ui) [arrow] Vi are toroidal for all i. [function] is then called locally toroidal. It is proved that a locally toroidal morphism from an arbitrary variety to a surface is toroidalizable.en_US
dc.identifier.merlin.b68801762en_US
dc.identifier.oclc374374524en_US
dc.identifier.otherHanumanthuK-050208-9420en_US
dc.identifier.urihttp://hdl.handle.net/10355/5608
dc.publisherUniversity of Missouri--Columbiaen_US
dc.relation.ispartof2008 Freely available dissertations (MU)en_US
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2008 Dissertations
dc.subject.lcshToroidal harmonicsen_US
dc.subject.lcshMorphisms (Mathematics)en_US
dc.titleToroidalization of locally toroidal morphismsen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineMathematicseng
thesis.degree.grantorUniversity of Missouri--Columbiaen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePh. D.en_US


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