Mirror symmetry, constructible sheaves and toric varieties
by Fang, Bohan, Ph.D., NORTHWESTERN UNIVERSITY, 2010, 99 pages; 3402153

Abstract:

This thesis explores the relation between three quasi-equivalent categories: the category of coherent sheaves on a toric variety, the category of certain constructible sheaves on a real vector space, and a certain Fukaya category of the cotangent bundle of that real vector space. The quasi-equivalence between the Fukaya category and the category of coherent sheaves is achieved by a T-duality process and is regarded as a version of homological mirror symmetry, while the quasi-equivalence between the category of certain constructible sheaves and the category of coherent sheaves is a new relation called coherent-constructible correspondence, which categorifies Morelli's theorem at the level of K-theory [Mo].

 
AdviserEric Zaslow
SchoolNORTHWESTERN UNIVERSITY
SourceDAI/B 71-05, p. , Jun 2010
Source TypeDissertation
SubjectsMathematics
Publication Number3402153
Adobe PDF Access the complete dissertation:
 

» Find an electronic copy at your library.
  Use the link below to access a full citation record of this graduate work:
  http://gateway.proquest.com/openurl%3furl_ver=Z39.88-2004%26res_dat=xri:pqdiss%26rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation%26rft_dat=xri:pqdiss:3402153
  If your library subscribes to the ProQuest Dissertations & Theses (PQDT) database, you may be entitled to a free electronic version of this graduate work. If not, you will have the option to purchase one, and access a 24 page preview for free (if available).

About ProQuest Dissertations & Theses
With over 2.3 million records, the ProQuest Dissertations & Theses (PQDT) database is the most comprehensive collection of dissertations and theses in the world. It is the database of record for graduate research.

The database includes citations of graduate works ranging from the first U.S. dissertation, accepted in 1861, to those accepted as recently as last semester. Of the 2.3 million graduate works included in the database, ProQuest offers more than 1.9 million in full text formats. Of those, over 860,000 are available in PDF format. More than 60,000 dissertations and theses are added to the database each year.

If you have questions, please feel free to visit the ProQuest Web site - http://www.proquest.com - or call ProQuest Hotline Customer Support at 1-800-521-3042.