Geodesic
Multiple mirrors and the JKLMR conjecture
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 149-162 Cet article a éte moissonné depuis la source Math-Net.Ru

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We address the problem of the fulfillment of the conjecture proposed by Jockers et al. (JKLMR conjecture) on the equality of the partition function of a supersymmetric gauged linear sigma model on the sphere $S^2$ and the exponential of the Kähler potential on the moduli space of Calabi–Yau manifolds. The problem is considered for a specific class of Calabi–Yau manifolds that does not belong to the Fermat type class. We show that the JKLMR conjecture holds when a Calabi–Yau manifold $X(1)$ of such type has a mirror partner $Y(1)$ in a weighted projective space that also admits a Calabi–Yau manifold of Fermat type $Y(2)$. Moreover, the mirror $X(2)$ for $Y(2)$ has the same special geometry on the moduli space of complex structures as the original $X(1)$.
Keywords: Calabi–Yau manifold, mirror symmetry, multiple mirrors
Mots-clés : Calabi–Yau moduli space. 
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A. A. Belavin; B. A. Eremin. Multiple mirrors and the JKLMR conjecture. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 149-162. http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a8/

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