Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The Pfaffian-Grassmannian derived equivalence


Authors: Lev Borisov and Andrei Caldararu
Journal: J. Algebraic Geom. 18 (2009), 201-222
DOI: https://doi.org/10.1090/S1056-3911-08-00496-7
Published electronically: March 17, 2008
MathSciNet review: 2475813
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Abstract | References | Additional Information

Abstract: We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking dual hyperplane sections (of the appropriate codimension) of the Grassmannian $ \mathbf{G}(2,7)$ and the Pfaffian $ \mathbf{Pf}(7)$. The existence of such an equivalence has been conjectured by physicists for almost ten years, as the two families of Calabi-Yau threefolds are believed to have the same mirror. It is the first example of a derived equivalence between non-birational Calabi-Yau threefolds.


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Additional Information

Lev Borisov
Affiliation: Mathematics Department, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, Wisconsin 53706–1388
Email: borisov@math.wisc.edu

Andrei Caldararu
Affiliation: Mathematics Department, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, Wisconsin 53706–1388
Email: andreic@math.wisc.edu

DOI: https://doi.org/10.1090/S1056-3911-08-00496-7
Received by editor(s): December 13, 2006
Received by editor(s) in revised form: June 9, 2007
Published electronically: March 17, 2008
Additional Notes: This material is based upon work supported by the National Science Foundation under Grants No. DMS-0456801 and DMS-0556042

American Mathematical Society