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Higgs triples and ruled surfaces / Michail Gerapetritis.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Gerapetritis, Michail, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Genre:
- Academic theses.
- Physical Description:
- 1 online resource (82 pages)
- Contained In:
- Dissertations Abstracts International 82-03B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2020.
- Language Note:
- English
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- Aiming to understand complexes of coherent sheaves on algebraic Poisson surfaces and the associated deformation quantizations and moduli problems, we begin our study by examining the case of ruled surfaces over a smooth projective curve $X$, namely the Poisson surface will be $S=\\mathbb{P}(\\mathcal{O}\\oplus\\omega)$, where $\\omega$ is the canonical line bundle of $X$. Fixing a vector bundle $F\o X$, after revisiting the background technology of \extsl{spectral data and Higgs bundles} we aim to encode $(D,\\,F)$-framed sheaves on $S$ as a form of \extsl{extended Higgs data} [Chapter 3], i.e. Higgs triples, as introduced by A. Minets , and $F$-prolonged Higgs bundles. We present our first main result, demonstrating the correspondence between pure $F$-prolonged Higgs bundles on $X$ and $(D,\\,F)$-framed torsion free sheaves on $S$, globally generated along the fibers of the natural projection. Moreover, exploring the close relation between the two types of extended Higgs data, we aim to place them in the context of perverse coherent sheaves on $X$ and examine the stability of the Higgs data as a polynomial stability in the sense of Bayer \\cite{bayer}. So, using the polynomial stability given by the dual to the large volume perversity, we recover the notion of stability for Higgs triples as introduced by Minets, but also derive a stability condition for (pure) $F$-prolonged Higgs bundles, so the stable objects correspond to Huybrechts-Lehn stable $(D,\\, F)$-framed torsion free sheaves.
- Notes:
- Source: Dissertations Abstracts International, Volume: 82-03, Section: B.
- Advisors: Pantev, Tony; Committee members: Ron Donagi; Jonathan Block.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2020.
- Local Notes:
- School code: 0175
- ISBN:
- 9798672110110
- Access Restriction:
- Restricted for use by site license.
- This item must not be sold to any third party vendors.
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