2026-09-20T04:43:32Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1269292026-06-16T18:53:21Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
.
Makarova, Svetlana,Ph. D.Massachusetts Institute of Technology.
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2020-09-03T16:41:16Z
2020-09-03T16:41:16Z
2020
2020
https://hdl.handle.net/1721.1/126929
1191267231
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 75-77).
The Strange Duality is a conjectural duality between two spaces of global sections of natural line bundles on moduli spaces of sheaves on a fixed variety. It has been proved in full generality on curves by Marian and Oprea, and by Belkale. There have been ongoing work on the Strange Duality on surfaces by various people. In the current paper, we show that the approach of Marian and Oprea to treating elliptic surfaces can be generalized in multiple directions: first, we can prove the Strange Duality in many cases over elliptic surfaces, and then, we extend their moduli construction to the non-ample quasipolarized locus of K3 surfaces.
by Svetlana Makarova.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
77 pages
eng
Massachusetts Institute of Technology
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Strange duality on elliptic and K3 surfaces
Thesis
application/pdf
2020-09-03T16:41:16Z
Publication
Doctoral
Math
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="23919912-e6d0-4bbe-8f24-035234108f70">
<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>Strange duality on elliptic and K3 surfaces</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2020</PublicationDate>
<Authors>
<Author>
<DisplayName>Makarova, Svetlana,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>Mathematics.</Keyword>
<Abstract>The Strange Duality is a conjectural duality between two spaces of global sections of natural line bundles on moduli spaces of sheaves on a fixed variety. It has been proved in full generality on curves by Marian and Oprea, and by Belkale. There have been ongoing work on the Strange Duality on surfaces by various people. In the current paper, we show that the approach of Marian and Oprea to treating elliptic surfaces can be generalized in multiple directions: first, we can prove the Strange Duality in many cases over elliptic surfaces, and then, we extend their moduli construction to the non-ample quasipolarized locus of K3 surfaces.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>