 

Mamoru Doi and Naoto Yotsutani
Doubling construction of CalabiYau threefolds view print


Published: 
December 6, 2014 
Keywords: 
Ricciflat metrics, CalabiYau manifolds, G_{2}structures, gluing, doubling. 
Subject: 
Primary: 53C25, Secondary: 14J32 


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


Acknowledgements
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:
119302 Yumotocho, Takarazuka, Hyogo 6650003, Japan
doi.mamoru@gmail.com
Naoto Yotsutani:
School of Mathematical Sciences at Fudan University, Shanghai, 200433, P. R. China
naotoyotsutani@fudan.edu.cn

