Minimal Resolution Conjecture in multiprojective spaces

Determine whether the Minimal Resolution Conjecture holds for sets of points in multiprojective spaces, including products of projective spaces such as P^n × P^m.

Background

The Minimal Resolution Conjecture (MRC), originally formulated for points in projective space, predicts non-overlapping patterns of graded Betti numbers for sufficiently general points. While some special cases are known (e.g., points on smooth quadrics in P^3), the general validity of MRC in multiprojective settings remains unresolved.

This paper relies on a weakened form of MRC tailored to P × P to construct explicit short virtual resolutions; the authors note that the full MRC remains open in multiprojective contexts.