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Quantum Cohomology of a Pfaffian Calabi–Yau Variety: Verifying Mirror Symmetry Predictions

Published online by Cambridge University Press:  04 December 2007

Erik N. Tjøtta
Erik N. Tjøtta
Affiliation:
University of Bergen, Institute of Mathematics, University of Bergen, 5007 Bergen, Norway. E-mail: erik.tjotta@mi.uib.no
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Abstract

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We formulate a generalization of Givental–Kim's quantum hyperplane principle. This is applied to compute the quantum cohomology of a Calabi–Yau 3-fold defined as the rank 4 locus of a general skew-symmetric 7×7 matrix with coefficients in P6. The computation verifies the mirror symmetry predictions of Rødland [25].

Keywords

PfaffianCalabi–Yaumirror symmetryquantum cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 1 , March 2001 , pp. 79 - 89
Copyright
© 2001 Kluwer Academic Publishers