Strange duality on elliptic and K3 surfaces

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Makarova, Svetlana,Ph. D.Massachusetts Institute of Technology.

Advisor dc:contributor.advisor

• .

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126929

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126929