ON THE CONTACT COHOMOLOGY OF ISOLATED HYPERSURFACE SINGULARITIES |
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Authors: | Xiao Erjian |
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Institution: | Institute of Mathematics, Fudan University, Shanghai 200433, China. |
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Abstract: | The author defines, using jets, cohomology $H^p(\Lambda _{f,k-})$ for hypersurfaces, which are invariant under contact transformations. For isolated hypersurface singularities, it is proved that
$H^0(\Lambda _{f,k-})=O_{U,0}/f^{k+1}O_{U,0},$
$H^p(\Lambda _{f,k-})=0,1\leq p \leq N-3 or p=N,$
$dimH^{N-2}(\Lambda _{f,k-})-dimH^{N-1}(\Lambda _{f,k-})=\\left( {\begin{array}{*{20}{c}}
k \ N
\end{array}} \right)\dim {O_{U,0}}/(f,\frac{{\partial f}}{{\partial {x_1}}}, \cdots ,\frac{{\partial f}}{{\partial {x_N}}}){O_{U,0}}\] $
The algorithm of computation for H^{N-2} and H^{N-1} is given, and it is proved that $H^{N-1}=0$ when f is quasi-homogeneous. |
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Keywords: | |
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