Desingularizing the boundary of the moduli space of genus one stable quotients

Persistent Link:
http://hdl.handle.net/10150/325213
Title:
Desingularizing the boundary of the moduli space of genus one stable quotients
Author:
Maienschein, Thomas Daniel
Issue Date:
2014
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The moduli space of stable quotients, introduced by Marian, Oprea, and Pandharipande, provides a nonsingular compactification of the moduli space of degree d maps from smooth genus 1 curves into projective space ℙⁿ. This is done by allowing the domain curve to have nodal singularities and by admitting certain rational maps. The rational maps are introduced in the following way: A map to projective space can be defined by a quotient bundle of the trivial bundle on the domain curve; in the compactification, the quotient bundle is replaced by a sheaf which may not be locally free. The boundary is filtered by the degree of the torsion subsheaf of the quotient. Yijun Shao has defined a similar compactification of the moduli space of degree d maps from ℙ¹ into a Grassmannian. A blow-up process is carried out on the compactification in order to produce a boundary which is a simple normal crossings divisor: The closed subschemes in the filtration of the boundary are blown up in order of decreasing torsion. In this thesis, we carry out an analogous blow-up process on the moduli space of stable quotients. We show that the end result is a nonsingular compactification which has as its boundary a simple normal crossings divisor.
Type:
text; Electronic Dissertation
Keywords:
quot schemes; stable maps; stable quotients; Mathematics; moduli spaces
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Hu, Yi

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleDesingularizing the boundary of the moduli space of genus one stable quotientsen_US
dc.creatorMaienschein, Thomas Danielen_US
dc.contributor.authorMaienschein, Thomas Danielen_US
dc.date.issued2014-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe moduli space of stable quotients, introduced by Marian, Oprea, and Pandharipande, provides a nonsingular compactification of the moduli space of degree d maps from smooth genus 1 curves into projective space ℙⁿ. This is done by allowing the domain curve to have nodal singularities and by admitting certain rational maps. The rational maps are introduced in the following way: A map to projective space can be defined by a quotient bundle of the trivial bundle on the domain curve; in the compactification, the quotient bundle is replaced by a sheaf which may not be locally free. The boundary is filtered by the degree of the torsion subsheaf of the quotient. Yijun Shao has defined a similar compactification of the moduli space of degree d maps from ℙ¹ into a Grassmannian. A blow-up process is carried out on the compactification in order to produce a boundary which is a simple normal crossings divisor: The closed subschemes in the filtration of the boundary are blown up in order of decreasing torsion. In this thesis, we carry out an analogous blow-up process on the moduli space of stable quotients. We show that the end result is a nonsingular compactification which has as its boundary a simple normal crossings divisor.en_US
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectquot schemesen_US
dc.subjectstable mapsen_US
dc.subjectstable quotientsen_US
dc.subjectMathematicsen_US
dc.subjectmoduli spacesen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorHu, Yien_US
dc.contributor.committeememberHu, Yien_US
dc.contributor.committeememberJoshi, Kirtien_US
dc.contributor.committeememberPickrell, Dougen_US
dc.contributor.committeememberCherkis, Sergeyen_US
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