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Ricci-Flat Mirror Hypersurfaces in Spaces of General Type

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arxiv 2501.11684 v1 pith:VFLK4DU2 submitted 2025-01-20 hep-th math.AG

Tristan Hübsch This is my paper · ORCID
classification hep-thmath.AG
keywords hypersurfacesencodedgeneralmirrorricci-flatspacestypeadmitting
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abstract

Complex Ricci-flat (i.e., Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) $U(1)^n$ gauge symmetry of general type (encoded by certain non-convex and multi-layered multitopes) may degenerate, but can be smoothed by rational (Laurent) anticanonical sections. Nevertheless, the phases of the Gauged Linear Sigma Model and an increasing number of their classical and quantum data are just as computable as for their siblings encoded by reflexive polytopes, and they all have transposition mirror models. Showcasing such hypersurfaces in so-called Hirzebruch scrolls shows this class of constructions to be infinitely vast, yet amenable to standard and well-founded algebro-geometric methods of analysis.

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  1. Beyond Algebraic Superstring Compactification

    hep-th 2025-02 conditional novelty 5.0 of 10

    Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.

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