Borcea-Voisin Calabi-Yau threefolds and invertible potentials
Michela Artebani, Samuel Boissi\`ere, Alessandra Sarti
TL;DR
This paper demonstrates that Borcea-Voisin Calabi-Yau threefolds and their mirrors, constructed via Berglund-H"ubsch-Chiodo-Ruan transposition, are birationally equivalent, confirming the consistency of mirror symmetry in this context.
Contribution
It proves that Borcea-Voisin mirror pairs can be modeled to satisfy the transposition rule, unifying two mirror construction methods for Calabi-Yau threefolds.
Findings
Mirror pairs admit projective birational models
Mirror constructions yield the same pairs under certain conditions
Supports the validity of the transposition rule in mirror symmetry
Abstract
We prove that the Borcea-Voisin mirror pairs of Calabi-Yau threefolds admit projective birational models that satisfy the Berglund-H\"ubsch-Chiodo-Ruan transposition rule. This shows that the two mirror constructions provide the same mirror pairs, as soon as both can be defined.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Black Holes and Theoretical Physics