J. Korean Math. Soc. 2003; 40(4): 667-680
Printed July 1, 2003
Copyright © The Korean Mathematical Society.
Takao Akahori
Himeji Institute of Technology
The mirror conjecture means originally the deep relation between complex and symplectic geometry in Calabi-Yau manifolds. Recently, this conjecture is posed beyond Calabi-Yau, and even for open manifolds (e.g. $A_n$ singularities and its resolution) is discussed. While if we treat open manifolds, we can't avoid the boundary (in our case, CR manifolds). Therefore we pose the more precise conjecture (mirror symmetry with boundaries). Namely, in mirror symmetry, for boundaries, what kind of structure should correspond? For this problem, the $A_n$ case is studied.
Keywords: symplectic geometry, isolated singularities, CR stru-ctures
MSC numbers: 32S, 32V
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd