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Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory. (English) Zbl 1360.14109
Kerr, Matt (ed.) et al., Recent advances in Hodge theory. Period domains, algebraic cycles, and arithmetic. Proceedings of the summer school and conference, University of British Columbia, Vancouver, Canada, June 10–20, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-54629-5/pbk; 978-1-316-38788-7/ebook). London Mathematical Society Lecture Note Series 427, 134-164 (2016).
Summary: We correct the definitions and descriptions of the integral structures by the author [A study of mirror symmetry through log mixed Hodge theory. Contemporary Mathematics 608, 285–311 (2014; Zbl 1314.14018)]. The previous flat basis by the author [loc. cit.] is characterized by the Frobenius solutions and is integral in the first approximation by mean of the graded quotients of monodromy filtration, but it is not integral in the strict sense.
In this article, we use \(\widehat\Gamma\)-integral structure of by H. Iritani [Ann. Inst. Fourier 61, No. 7, 2909–2958 (2011; Zbl 1300.14055)] for A-model. Using this precise version, we study open mirror symmetry for quintic threefolds through log mixed Hodge theory, especially the recent result on Néron models for admissible normal functions with non-torsion extensions in the joint work [Proc. Japan Acad., Ser. A 90, No. 1, 6–10 (2014; Zbl 1303.14022)] with K. Kato and C. Nakayama. We understand asymptotic conditions as values in the fiber over a base point on the boundary of \(S^{\log}\).
For the entire collection see [Zbl 1348.14004].
14J33 Mirror symmetry (algebro-geometric aspects)
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D07 Variation of Hodge structures (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations