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virtual fundamental class

\([X/Y] = f { ! }\in H_{2d}^{{\operatorname{BM}}}(X/Y; {\mathbf{Q}}(d))\) where \(1\in H_0^{{\operatorname{BM}}}(Y/Y; {\mathbf{Q}})\).

See Alexander duality, Kuranishi charts.

For moduli spaces

See construction of global Kuranishi charts.