Doubling construction of Calabi-Yau threefolds

摘要

We give a differential-geometric construction and examples of Calabi-Yau threefolds, at least one of which is new.Ingredients in our construction are admissible pairs, which were dealt with by Kovalev, 2003,and further studied by Kovalev and Lee, 2011.An admissible pair (ar{X},D) consists ofa three-dimensional compact Kähler manifold ar{X} anda smooth anticanonical K3 divisor D on ar{X}.If two admissible pairs (ar{X}1,D1) and (ar{X}2,D2) satisfythe gluing condition, we can glue ar{X}1setminus D1 andar{X}2setminus D2 together to obtain a Calabi-Yau threefold M.In particular, if (ar{X}1,D1) and (ar{X}2,D2)are identical to an admissible pair (ar{X},D),then the gluing condition holds automatically, so that we can always constructa Calabi-Yau threefold from a single admissible pair (ar{X},D)by doubling it.Furthermore, we can compute all Betti and Hodge numbers of the resulting Calabi-Yau threefoldsin the doubling construction.