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 $${\mathbb {Q}}$$ Q -Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using $$\bar{\partial }$$ ∂ ¯ -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.