RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Main page
About this project
Software
Classifications
Links
Terms of Use

Search papers
Search references

RSS
Current issues
Archive issues
What is RSS






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


J. Am. Math. Soc., 2013, Volume 26, Issue 4, Pages 1051–1083 (Mi jams2)  

Homological mirror symmetry for punctured spheres

M. Abouzaida, D. Aurouxb, A. I. Efimovc, L. Katzarkovde, D. Orlovc

a Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
b Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
c Algebraic Geometry Section, Steklov Mathematical Institute, Russian Academy of Sciences, 8 Gubkin Street, Moscow 119991, Russia
d Department of Mathematics, Universität Wien, Garnisongasse 3, Vienna A-1090, Austria
e University of Miami, P.O. Box 249085, Coral Gables, Florida 33124-4250

Abstract: We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2}$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the Landau–Ginzburg model.

Funding Agency Grant Number
National Science Foundation DMS-0652630
DMS-1007177
DMS-0600800
DMS-0652633
Dynasty Foundation
4713.2010.1
Ministry of Education and Science of the Russian Federation 11.G34.31.0023
Austrian Science Fund P20778
European Research Council GEMIS
Russian Foundation for Basic Research 10-01-93113
11-01-00336
11-01-00568
The first author was supported by a Clay Research Fellowship. The second author was partially supported by NSF grants DMS-0652630 and DMS-1007177. The third author was partially supported by the Dynasty Foundation, NSh grant 4713.2010.1, and by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023. The fourth author was funded by NSF grant DMS-0600800, NSF FRG grant DMS-0652633, FWF grant P20778, and an ERC grant Ц GEMIS. The last author was partially supported by RFBR grants 10-01-93113, 11-01-00336, 11-01-00568, NSh grant 4713.2010.1, and by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023.


DOI: https://doi.org/10.1090/S0894-0347-2013-00770-5


Bibliographic databases:

Document Type: Article
MSC: Primary 53D37, 14J33; Secondary 53D40, 53D12, 18E30, 14F05
Received: 22.03.2011
Revised: 02.03.2013
Language: English

Linking options:
  • http://mi.mathnet.ru/eng/jams2

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:45

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018