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Iskovskikh Seminar
May 15, 2014 18:00, Moscow, Steklov Mathematical Institute, room 540
 


Calabi–Yau threefolds: Age of Discovery?

S. Galkinab

a Moscow Institute of Physics and Technology
b Department of Mathematics, National Research University "Higher School of Economics"

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Abstract: I'll give a brief overview of the so far discovered borders in the geography of Calabi–Yau threefolds. Mostly I'll be concerned with two (conjecturally almost symmetric) borders: Calabi–Yau threefolds with Picard number one (and also with the related question of Fano fourfolds with Picard number one), and Calabi–Yau threefolds with one-dimensional moduli space (also rigid Calabi–Yau threefolds, that violate mirror symmetry).
I know about a hundred examples, including some hypothetical, and about fifty examples that I am confident in.
There are less than ten various constructions, that Ill try to review.
Time permits, Ill tell some new constructions that produce about a dozen new examples (or realize some of the old hypotheses).

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