The Pfaffian-Grassmannian derived equivalence

Details The Pfaffian-Grassmannian derived equivalence The Pfaffian-Grassmannian derived equivalence

2006-08-15

arxiv.org/abs/math/0608404v3

Mathematics

Algebraic Geometry

Streamlined and shortened exposition, Macaulay calculations not needed any more

Scientific paper

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) and the Pfaffian 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 Calabi-Yau threefolds which are provably non-birational.

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