A Pardon Algebra for Zero-cycles

Abstract

Recently, John Pardon proved the MNOP conjecture (on the GW-DT correspondence for CY3s) by introducing a new mathematical gadget, which we call the Pardon homology algebra of 1-cycles in 3-folds. We work out an analogous construction for 0-cycles in d-folds. This gives a new point of view on enumerative problems involving point-counting, such as, for example, the degree zero MNOP conjecture on the Hilbert scheme of points in projective 3-folds.