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.
Mirror symmetry and projective geometry of Reye congruences I
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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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A single point as a Calabi-Yau zerofold
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.