 First, using the regular sequence of functions defining "M"0 inside "M", construct a Koszul complex

The differential, δ, on this complex is an odd "C"∞("M")-linear derivation of the graded "C"∞("M")-algebra formula_15.This odd derivation is defined by extending the Lie algebra homomorphim formula_16 of the hamiltonian action.The resulting Koszul complex is the Koszul complex of the formula_17-module "C"∞("M"), where formula_18 is the symmetric algebra of formula_8, and the module structure comes from a ring homomorphism formula_20 induced by the hamiltonian action formula_21.