2026-09-18T21:13:49Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1245932026-06-16T18:53:55Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Washington Taylor, IV.
Huang, Yu-Chien,Ph. D.Massachusetts Institute of Technology.
Massachusetts Institute of Technology. Department of Physics.
Massachusetts Institute of Technology. Department of Physics
2020-04-13T18:33:04Z
2020-04-13T18:33:04Z
2019
2019
https://hdl.handle.net/1721.1/124593
1149091076
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 245-255).
In this thesis, we investigate the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau three folds by (1) constructing explicitly elliptically fibered Calabi-Yau threefolds with large Hodge numbers using Weierstrass model techniques motivated by F-theory, and comparing the Tate-tuned Wierstrass model set with the set of Calabi-Yau threefolds constructed using toric hypersurface methods, and (2) systematically analyzing directly the fibration structure of 4D reflexive polytopes by classifying all the 2D subpolytopes of the 4D polytopes in the Kreuzer and Skarke database of toric Calabi-Yau hypersurfaces. With the classification of the 2D fibers, we then study the mirror symmetry structure of elliptic toric hypersurface Calabi-Yau threefolds. We show that the mirror symmetry of Calabi-Yau manifolds factorizes between the toric fiber and the base: if there exist 2D mirror fibers of a pair of mirror reflexive polytopes, the base and fibration structure of one hypersurface Calabi-Yau determine the base of the other.
by Yu-Chien Huang.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Physics
255 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Physics.
Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations
Thesis
application/pdf
2020-04-13T18:32:35Z
Publication
Doctoral
Phys
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="30d6bf0c-4356-47a0-abe7-503e70371977">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2019</PublicationDate>
<Authors>
<Author>
<DisplayName>Huang, Yu-Chien,Ph. D.Massachusetts Institute of Technology.</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Physics.</Keyword>
<Abstract>In this thesis, we investigate the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau three folds by (1) constructing explicitly elliptically fibered Calabi-Yau threefolds with large Hodge numbers using Weierstrass model techniques motivated by F-theory, and comparing the Tate-tuned Wierstrass model set with the set of Calabi-Yau threefolds constructed using toric hypersurface methods, and (2) systematically analyzing directly the fibration structure of 4D reflexive polytopes by classifying all the 2D subpolytopes of the 4D polytopes in the Kreuzer and Skarke database of toric Calabi-Yau hypersurfaces. With the classification of the 2D fibers, we then study the mirror symmetry structure of elliptic toric hypersurface Calabi-Yau threefolds. We show that the mirror symmetry of Calabi-Yau manifolds factorizes between the toric fiber and the base: if there exist 2D mirror fibers of a pair of mirror reflexive polytopes, the base and fibration structure of one hypersurface Calabi-Yau determine the base of the other.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>