Polynomial interpolation and residue currents

Journal article, 2022

We show that a global holomorphic section of O(d) restricted to a closed complex subspace X subset of P-n has an interpolant if and only if it satisfies a set of moment conditions that involves a residue current associated with a locally free resolution of O-X. When X is a finite set of points in C-n subset of P-n this can be interpreted as a set of linear conditions that a function on X has to satisfy in order to have a polynomial interpolant of degree at most d.