Toroidalization of locally toroidal morphisms

MOspace/Manakin Repository

Breadcrumbs Navigation

Toroidalization of locally toroidal morphisms

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/5608

[-] show simple item record

dc.contributor.advisor Cutkosky, Steven Dale en
dc.contributor.author Hanumanthu, Krishna Chaithanya, 1981- en_US
dc.date.accessioned 2010-02-23T16:35:00Z
dc.date.available 2010-02-23T16:35:00Z
dc.date.issued 2008 en_US
dc.date.submitted 2008 Spring en
dc.identifier.other HanumanthuK-050208-9420 en_US
dc.identifier.uri http://hdl.handle.net/10355/5608
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. en_US
dc.description Title from title screen of research.pdf file (viewed on June 8, 2009) en_US
dc.description Vita. en_US
dc.description Includes bibliographical references. en_US
dc.description Thesis (Ph. D.) University of Missouri-Columbia 2008. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Mathematics. en_US
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. en_US
dc.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2008 Freely available dissertations (MU) en_US
dc.subject.lcsh Toroidal harmonics en_US
dc.subject.lcsh Morphisms (Mathematics) en_US
dc.title Toroidalization of locally toroidal morphisms en_US
dc.type Thesis en_US
thesis.degree.discipline Mathematics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name Ph. D. en_US
thesis.degree.level Doctoral en_US
dc.identifier.merlin .b68801762 en_US
dc.identifier.oclc 374374524 en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2008 Dissertations


This item appears in the following Collection(s)

[-] show simple item record