New York Journal of Mathematics
Volume 20 (2014) 1203-1235


Mamoru Doi and Naoto Yotsutani

Doubling construction of Calabi-Yau threefolds

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Published: December 6, 2014
Keywords: Ricci-flat metrics, Calabi-Yau manifolds, G2-structures, gluing, doubling.
Subject: Primary: 53C25, Secondary: 14J32

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 (\bar{X},D) consists of a three-dimensional compact Kähler manifold \bar{X} and a smooth anticanonical K3 divisor D on \bar{X}. If two admissible pairs (\bar{X}1,D1) and (\bar{X}2,D2) satisfy the gluing condition, we can glue \bar{X}1\setminus D1 and \bar{X}2\setminus D2 together to obtain a Calabi-Yau threefold M. In particular, if (\bar{X}1,D1) and (\bar{X}2,D2) are identical to an admissible pair (\bar{X},D), then the gluing condition holds automatically, so that we can always construct a Calabi-Yau threefold from a single admissible pair (\bar{X},D) by doubling it. Furthermore, we can compute all Betti and Hodge numbers of the resulting Calabi-Yau threefolds in the doubling construction.


The second author is partially supported by the China Postdoctoral Science Foundation Grant, No. 2011M501045 and the Chinese Academy of Sciences Fellowships for Young International Scientists 2011Y1JB05.

Author information

Mamoru Doi:
11-9-302 Yumoto-cho, Takarazuka, Hyogo 665-0003, Japan

Naoto Yotsutani:
School of Mathematical Sciences at Fudan University, Shanghai, 200433, P. R. China