Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2003; 40(4): 667-680

Printed July 1, 2003

Copyright © The Korean Mathematical Society.

Homogeneous polynomial hypersurface isolated singularities

Takao Akahori

Himeji Institute of Technology

Abstract

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

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