Geometric invariants from the resolution for the quotient module along a multi dimentional grid

Abstract

We construct a resolution for certain class of quotient modules of a Hilbert module consisting of holomorphic functions on a bounded open connected set Ω ⊆ C^m. Each one of these quotient modules is obtained from the submodule of all functions vanishing on an analytic variety Z ⊆ Ω using a multi-dimensional grid. A construction of the fundamental class of the variety Z using this resolution is given. The relationship of the resolution for the quotient module with the Koszul complex is also explicitly described.