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The Pfaffian Calabi–Yau, its Mirror, and their Link to the Grassmannian G(2,7)

Published online by Cambridge University Press:  04 December 2007

Einar Andreas Rødland
Einar Andreas Rødland
Affiliation:
Department of Mathematics, University of Oslo, Box 1053 Blindern, 0316 Oslo, Norway. E-mail: [email protected]
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Abstract

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The rank 4 locus of a general skew-symmetric 7 × 7 matrix gives the Pfaffian variety in P20 which is not defined as a complete intersection. Intersecting this with a general P6 gives a Calabi–Yau manifold. An orbifold construction seems to give the 1-parameter mirror-family of this. However, corresponding to two points in the 1-parameter family of complex structures, both with maximally unipotent monodromy, are two different mirror-maps: one corresponding to the general Pfaffian section, the other to a general intersection of G(2,7) ⊂ P20 with a P13. Apparently, the Pfaffian and G(2,7) sections constitute different parts of the A-model (Kähler structure related) moduli space, and, thus, represent different parts of the same conformal field theory moduli space.

Keywords

Calabi–Yau 3-foldsmirror symmetryPicard–Fuchs equation
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 2 , June 2000 , pp. 135 - 149
Copyright
© 2000 Kluwer Academic Publishers