Residue currents and fundamental cycles

Abstract

We give a factorization of the fundamental cycle of an analytic space in terms of certain differential forms and residue currents associated with a locally free resolution of its structure sheaf. Our result can be seen as a generalization of the classical Poincaré-Lelong formula. It is also a current version of a result by Lejeune-Jalabert, who similarly expressed the fundamental class of a Cohen-Macaulay analytic space in terms of differential forms and cohomological residues.

24 pages

References in corpus (4)

• A comparison formula for residue currents
• A local Grothendieck duality theorem for Cohen-Macaulay ideals
• A local duality principle for ideals of pure dimension
• Explicit versions of the local duality theorem in ${\mathbb{C}}^n$

Cited by in corpus (3)

• Residue currents and cycles of complexes of vector bundles
• Norm estimates for the $\bar{\partial }$-equation on a non-reduced space
• Chern currents of coherent sheaves