The Pfaffian-Grassmannian derived equivalence
- 17 March 2008
- journal article
- Published by American Mathematical Society (AMS) in Journal of Algebraic Geometry
- Vol. 18 (2) , 201-222
- https://doi.org/10.1090/s1056-3911-08-00496-7
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 G ( 2 , 7 ) \mathbf {G}(2,7) and the Pfaffian P f ( 7 ) \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.Keywords
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