Explicit determination of dualizing sheaves/complexes on singular spaces

Construct explicit formulas or general procedures to determine the dualizing sheaf or dualizing complex for singular algebraic varieties and related spaces, enabling explicit definitions of intersection products and duality pairings beyond the limited special cases where formulas are currently available.

Background

Grothendieck and Verdier dualities provide the appropriate abstract framework for intersection pairings, but their practical use relies on knowing the dualizing sheaf or dualizing complex explicitly. In many applications involving singular spaces, explicit descriptions are unavailable.

The authors highlight that only special classes admit closed-form expressions and that a general methodology is lacking, which obstructs direct computations of intersection products in broad settings.