Dolbeault Complex on S\{·} and S\{·} through Supersymmetric Glasses


S is not a complex manifold, but it is sufficient to remove one point to make it complex. Using supersymmetry methods, we show that the Dolbeault complex (involving the holomorphic exterior derivative ∂ and its Hermitian conjugate) can be perfectly well defined in this case. We calculate the spectrum of the Dolbeault Laplacian. It involves 3 bosonic zero modes such that the Dolbeault index on S\{·} is equal to 3.

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@inproceedings{Smilga2011DolbeaultCO, title={Dolbeault Complex on S\\{·\} and S\\{·\} through Supersymmetric Glasses}, author={Andrei V. Smilga}, year={2011} }