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

1999/06/18 by Erik N. Tjøtta, Erik N. Tjotta, Tjotta, Erik N.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9906119

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

openalex publication_date 1999/06/18 · arxiv created 2000/04/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 P6. The computation verifies the mirror symmetry predictions of Rødland in math.AG/9801092.

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