Kähler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere
Kähler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere
| dc.identifier.uri | http://hdl.handle.net/11401/76406 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | We start this work by reinterpreting the Moduli problem of stable parabolic bundles from a complex analytic perspective. This allows us to introduce canonical complex coordinates on the Moduli space, analogous to the Bers' coordinates on Teichmüller spaces. Similarly, a suitable analog of uniformization will play a central role. Finally, the identification of the tangent space at a point with a certain space of automorphic forms leads to the introduction of the parabolic Narasimhan-Atiyah-Bott metric on the Moduli space, which is analogous to the Weil-Petersson metric. Secondly, for each stable parabolic bundle, a regularized WZNW action functional is defined on the space of singular Hermitian metrics with prescribed asymptotics at a finite set of points in the sphere. We prove that these functionals evaluated at their extrema gives rise to a function on the Moduli space that is a Kähler potential for the parabolic Narasimhan-Atiyah-Bott metric over a certain analytic open subset. | |
| dcterms.abstract | We start this work by reinterpreting the Moduli problem of stable parabolic bundles from a complex analytic perspective. This allows us to introduce canonical complex coordinates on the Moduli space, analogous to the Bers' coordinates on Teichmüller spaces. Similarly, a suitable analog of uniformization will play a central role. Finally, the identification of the tangent space at a point with a certain space of automorphic forms leads to the introduction of the parabolic Narasimhan-Atiyah-Bott metric on the Moduli space, which is analogous to the Weil-Petersson metric. Secondly, for each stable parabolic bundle, a regularized WZNW action functional is defined on the space of singular Hermitian metrics with prescribed asymptotics at a finite set of points in the sphere. We prove that these functionals evaluated at their extrema gives rise to a function on the Moduli space that is a Kähler potential for the parabolic Narasimhan-Atiyah-Bott metric over a certain analytic open subset. | |
| dcterms.available | 2017-09-20T16:50:10Z | |
| dcterms.contributor | Takhtajan, Leon | en_US |
| dcterms.contributor | Starr, Jason | en_US |
| dcterms.contributor | Lyubich, Mikhail | en_US |
| dcterms.contributor | Kra, Irwin. | en_US |
| dcterms.creator | Meneses-Torres, Claudio | |
| dcterms.dateAccepted | 2017-09-20T16:50:10Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:10Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 107 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76406 | |
| dcterms.issued | 2013-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:10Z (GMT). No. of bitstreams: 1 MenesesTorres_grad.sunysb_0771E_11570.pdf: 864746 bytes, checksum: fe68f7576e1d246019b4db229de13b32 (MD5) Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | action functional, Kähler potential, Moduli, Parabolic bundle, Riemann sphere, singular Hermitian metric | |
| dcterms.subject | Mathematics | |
| dcterms.subject | action functional, Kähler potential, Moduli, Parabolic bundle, Riemann sphere, singular Hermitian metric | |
| dcterms.title | Kähler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere | |
| dcterms.title | Kähler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere | |
| dcterms.type | Dissertation |
