Topics in Higgs bundles and modules over even clifford algebra / Jia-Choon Lee.

Format:

Book

Thesis/Dissertation

Author/Creator:

Lee, Jia-Choon, author.

Contributor:

Donagi, Ron, degree supervisor.

Pantev, Tony, 1963- degree supervisor.

University of Pennsylvania. Department of Mathematics, degree granting institution.

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 (116 pages)

Contained In:

Dissertations Abstracts International 82-12B.

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2021.

Language Note:

English

System Details:

Mode of access: World Wide Web.

text file

Summary:

The first part of the thesis is a joint work with Sukjoo Lee. It was shown by Diaconescu, Donagi and Pantev that Hitchin systems of type ADE are isomorphic to certain Calabi-Yau integrable systems. In this paper, we prove an analogous result in the setting of meromorphic Hitchin systems of type A which are known to be Poisson integrable systems. We consider a symplectization of the meromorphic Hitchin integrable system, which is a semi-polarized integrable system in the sense ofKontsevich and Soibelman. On the Hitchin side, we show that the moduli space of unordered diagonally framed Higgs bundles forms an integrable system in this sense and recovers the meromorphic Hitchin system as the fiberwise compact quotient. Then we construct a new family of quasi-projective Calabi-Yau threefolds and show that its relative intermediate Jacobian fibration, as a semi-polarized integrable system, is isomorphic to the moduli space of unordered diagonally framed Higgs bundles.The second part of the thesis studies the relation between the moduli spaces of modules over the sheaf of even Clifford algebra and the Prym variety, both associated to a conic bundle. In particular, we construct a rational map from the moduli space of modules over the sheaf of even Clifford algebra to the special subvarieties in Prym varieties, and check that the rational map is birational in some cases. As an application, we get an explicit correspondence between instanton bundles on cubic threefolds and twisted Higgs bundles.

Notes:

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Advisors: Donagi, Ron; Pantev, Tony; Committee members: Jonathan Block; Ron Donagi; Tony Pantev.

Department: Mathematics.

Ph.D. University of Pennsylvania 2021.

Local Notes:

School code: 0175

ISBN:

9798738619304

Access Restriction:

Restricted for use by site license.

This item must not be sold to any third party vendors.