The Pfaffian-Grassmannian derived equivalence

By L. Borisov, Andrei Căldăraru. 2006

97 citations recorded by the source corpus.

We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking dual linear 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7bc26f77c3643a7ef36928b8c869224a21843822

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In Geometry and Topology

1. K. Hori
2. David Tong
3. C. Vafa
4. Marcos Mariño
5. F. Benini
6. Joaquim Gomis
7. Sungjay Lee
8. P. Seidel

In Mathematical Physics

1. David Tong
2. K. Hori
3. J. Louis
4. Thomas W. Grimm

Citations in the corpus

• Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories (2006, background): “The proof is also given independently in [41].”
• Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories (2011, methodology): “Proofs are given by Borisov-Caldararu [39] and Kuznetsov [40].”