dc.contributor.advisor | Cutkosky, Steven Dale | eng |
dc.contributor.author | Hanumanthu, Krishna Chaithanya, 1981- | eng |
dc.date.issued | 2008 | eng |
dc.date.submitted | 2008 Spring | eng |
dc.description | The 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. | eng |
dc.description | Title from title screen of research.pdf file (viewed on June 8, 2009) | eng |
dc.description | Vita. | eng |
dc.description | Includes bibliographical references. | eng |
dc.description | Thesis (Ph. D.) University of Missouri-Columbia 2008. | eng |
dc.description | Dissertations, Academic -- University of Missouri--Columbia -- Mathematics. | eng |
dc.description.abstract | Let 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. | eng |
dc.identifier.merlin | b68801762 | eng |
dc.identifier.oclc | 374374524 | eng |
dc.identifier.uri | http://hdl.handle.net/10355/5608 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartof | 2008 Freely available dissertations (MU) | eng |
dc.relation.ispartofcommunity | University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2008 Dissertations | eng |
dc.subject.lcsh | Toroidal harmonics | eng |
dc.subject.lcsh | Morphisms (Mathematics) | eng |
dc.title | Toroidalization of locally toroidal morphisms | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |