Show simple item record

dc.contributor.authorVicente Colmenares, Alejandra 12:45:15 (GMT) 12:45:15 (GMT)
dc.description.abstractIt has been observed by S. Rayan that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira classification. Motivated by this remark, we study the geometry of these objects (in the rank 2 case) over Hirzebruch surfaces, giving special emphasis to P^1 x P^1. Two main topics can be identified throughout the dissertation: non-emptiness of the moduli spaces of rank 2 semistable co-Higgs bundles over Hirzebruch surfaces, and the description of these moduli spaces over P^1 x P^1. The existence problem consists in determining for which pairs of Chern classes (c_1; c_2) there exists a non-trivial semistable rank 2 co-Higgs bundle with Chern classes c_1 and c_2. We approach this problem from two different perspectives. On one hand, we restrict ourselves to certain natural choices of c_1 and give necessary and sufficient conditions on c_2 that guarantee the existence of non-trivial semistable co-Higgs bundles with these Chern classes; we do this for arbitrary polarizations when c_2 ≤ 2. On the other hand, for arbitrary c_1, we also provide necessary and sufficient conditions on c_2 that ensure the existence of nontrivial semistable co-Higgs bundles; however, we only do this for the standard polarization. As for the description of the moduli spaces M(c_1; c_2) of rank 2 semistable co-Higgs bundles over P^1 x P^1, we restrict ourselves to the standard polarization. We then discuss how to use the spectral construction and the Hitchin correspondence to understand generic rank 2 semistable co-Higgs bundles. Furthermore, we give an explicit description of the moduli spaces when c_2 = 0; 1 for certain choices of c_1. Finally, we explore the first order deformations of points in the moduli space M(c_1; c_2).en
dc.publisherUniversity of Waterloo
dc.subjectPure Mathematicsen
dc.subjectComplex Geometryen
dc.subjectCo-Higgs Bundlesen
dc.subjectModuli Spacesen
dc.subjectHirzebruch Surfacesen
dc.titleSemistable rank 2 co-Higgs bundles over Hirzebruch surfacesen
dc.typeDoctoral Thesisen
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeDoctor of Philosophyen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages