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Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds.(English)Zbl 1509.14078

The authors introduce the notion of Kähler attractor mechanism of Kähler moduli space, and develop parallel theories to complex side. After constructing the mathematical foundations of complex attractor mechanism, the authors introduce Kähler attractor mechanism inspired by mirror symmetry.

MSC:

14J33 Mirror symmetry (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J28 \(K3\) surfaces and Enriques surfaces
53D05 Symplectic manifolds (general theory)
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category

Cite

References:

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[12]Hosono, S., Central charges, symplectic forms, and hypergeometric series in local mirror symmetry, (Mirror Symmetry. V. Mirror Symmetry. V, AMS/IP Stud. Adv. Math., vol. 38 (2006), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 405-439 ·Zbl 1114.14025
[13]Hulek, K.; Laface, R., On the Picard numbers of abelian varieties, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 19, 3, 1199-1224 (2019) ·Zbl 1429.14026
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[15]Iritani, H., An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math., 222, 1016-1079 (2009) ·Zbl 1190.14054
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[17]Kanazawa, A.; Lau, S.-C., Local Calabi-Yau manifolds of \(\widetilde{A}\) via SYZ mirror symmetry, J. Geom. Phys., 139, 103-138 (2019) ·Zbl 1417.53094
[18]Katzarkov, L.; Kontsevich, M.; Pantev, T., Hodge theoretic aspects of mirror symmetry, (From Hodge Theory to Integrability and TQFT \(t t^\ast \)-Geometry. From Hodge Theory to Integrability and TQFT \(t t^\ast \)-Geometry, Proc. Sympos. Pure Math., vol. 78 (2008), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 87-174 ·Zbl 1206.14009
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[27]Trenner, T.; Wilson, P. M.H., Asymptotic curvature of moduli spaces for Calabi-Yau threefolds, J. Geom. Anal., 21, 2, 409-428 (2011) ·Zbl 1226.14055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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