Tautological integrals on curvilinear Hilbert schemes

摘要

We take a new look at the curvilinear Hilbert scheme of points on a smooth projective variety X as a projective completion of the nonreductive quotient of holomorphic map germs from the complex line into X by polynomial reparametrisations. Using an algebraic model of this quotient coming from global singularity theory we develop an iterated residue formula for tautological integrals over curvilinear Hilbert schemes.