

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






Calabi–Yau threefolds: Age of Discovery?
S. Galkin^{ab} ^{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 onedimensional 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 I’ll try to review.
Time permits, I’ll tell some new constructions that produce about a dozen
new examples (or realize some of the old hypotheses).

