English

The Pfaffian-Grassmannian derived equivalence

Algebraic Geometry 2007-05-23 v3

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) 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.

Keywords

Cite

@article{arxiv.math/0608404,
  title  = {The Pfaffian-Grassmannian derived equivalence},
  author = {Lev Borisov and Andrei Caldararu},
  journal= {arXiv preprint arXiv:math/0608404},
  year   = {2007}
}

Comments

Streamlined and shortened exposition, Macaulay calculations not needed any more