On proper intersections on a singular analytic space

Abstract Given a reduced analytic space Y we introduce a class of nice cycles, including all effective $${\mathbb {Q}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> -Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using $$\bar{\partial }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mrow> <mml:mi>∂</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> -potentials and residue calculus we provide an intrinsic way of defining this product. The intrinsic definition makes it possible to prove global formulas. In case Y is smooth all cycles are differences of nice cycles, and so we get a new way to define classical proper intersections.