Quantum cohomology of a Pfaffian Calabi-Yau variety: verifying mirror symmetry predictions

Abstract

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 7x7 matrix with coeffisients in P^6. The computation verifies the mirror symmetry predictions of Rødland in math.AG/9801092.

10 pages. Minor modifications and references added. To appear in Compositio Mathematica

References in corpus (1)

• Rational Curves on the Space of Determinantal Nets of Conics

Cited by in corpus (5)

• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
• Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections
• Pfaffian Calabi-Yau Threefolds and Mirror Symmetry