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Aspects on Calabi-Yau moduli. (English) Zbl 1411.32019
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press. Adv. Lect. Math. (ALM) 42, 527-550 (2018).
Summary: This is a personal update on some recent advances on the geometry of moduli spaces of Calabi-Yau manifolds, especially along the finite distance boundary with respect to the Weil-Petersson metric. Two main themes are metric completion and extremal transitions. Besides reviewing the known results, I will also raise some related questions.
For the entire collection see [Zbl 1398.14003].
32Q25 Calabi-Yau theory (complex-analytic aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J15 Moduli, classification: analytic theory; relations with modular forms
32G13 Complex-analytic moduli problems
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry