2015/10/28 by Andrew Schaug, Schaug, Andrew
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP
paper · pdf · doi:10.48550/arxiv.1510.08333
13 pages
arxiv created 2015/10/28 · openalex publication_date 2015/10/28 · arxiv updated 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Borcea-Voisin threefolds provided some of the first examples of mirror pairs in the Hodge-theoretic sense, but their mirror symmetry at the quantum level have not previously been shown. We prove a Givental-style quantum mirror theorem for certain Borcea-Voisin threefolds: by means of certain birational models, we show that their Gromov-Witten J-functions are related by a mirror map to solutions of the multi-parameter Picard-Fuchs equations coming from the variation of Hodge structures of their mirror partners.