Quantum Mirror Symmetry for Borcea-Voisin Threefolds
Andrew Schaug
TL;DR
This paper establishes a quantum mirror symmetry theorem for Borcea-Voisin threefolds, linking their Gromov-Witten invariants to solutions of Picard-Fuchs equations, thus advancing the understanding of mirror symmetry at the quantum level.
Contribution
It proves a Givental-style quantum mirror theorem for Borcea-Voisin threefolds, connecting their Gromov-Witten invariants with mirror Hodge structures.
Findings
Gromov-Witten J-functions relate to mirror solutions via a mirror map
Quantum mirror symmetry is established for certain Borcea-Voisin threefolds
The results extend mirror symmetry understanding to the quantum level
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry