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Mirror symmetry and projective geometry of Reye congruences I

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arxiv 1101.2746 v2 pith:LFMSWAXE submitted 2011-01-14 math.AG

classification math.AG
keywords mirrorsymmetrycalabi-yaureyebranchedcalculatecompletecongruence
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abstract

Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$ branched over a curve. We also calculate BPS numbers of both $X$ and $Y$ (and also a related Calabi-Yau complete intersection $\tilde X_0$) using mirror symmetry.

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  1. A single point as a Calabi-Yau zerofold

    hep-th 2025-06 conditional novelty 4.0 of 10

    A single point is realized as the large-volume phase of a non-abelian GLSM, with a non-regular other phase, divergent partition function sums, and a matching mirror period.

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