Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HOMOGENEOUS POLYNOMIAL HYPERSURFACE ISOLATED SINGULARITIES

  • Akahori, Takao (Department of Mathematics Himeji Institute of Technology)
  • Published : 2003.07.01
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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 to, 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\ulcorner For this problem, the $A_{n}$ case is studied.

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References

  1. Invent. Math. v.63 no.2 The new estimate for the subbundles $E_j$ and its application to the deformation of the boundaries of strongly pseudoconvex domains T.Akahori https://doi.org/10.1007/BF01393881
  2. MSRI preprint 1996-026 A mixed Hodge structure on a CR manifold T.Akahori
  3. Michingan Math. J. v.50 Deformation theory of five-dimensional CR structures and the Rumin complex T.Akahori;P.M.Garfield;J.M.Lee https://doi.org/10.1307/mmj/1039029981
  4. The bigraded Rumin complex on CR manifolds T.Akahori
  5. On the ordinary double point from the point of view of CR structures T.Akahori;P.M.Garfield
  6. Compositio Math. v.85 no.1 An analogy of Tian-Todorov theorem on deformations of CR-structures T.Akahori;K.Miyajima
  7. Several complex variables;Proceedings of Symposia in Pure Mathematics v.XXX Application of $\overline(\partial)_b$to deformation of isolated singularities M.Kuranishi

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