Tautological integrals over curvilinear Hilbert schemes
Event details
| Date | 29.09.2015 |
| Hour | 15:15 › 17:00 |
| Speaker | Gergely Bérczi, (Oxford) |
| Location | |
| Category | Conferences - Seminars |
The punctual Hilbert scheme of k points on a smooth projective variety X parametrises zero dimensional subschemes of X of length k supported at one point. A point of the punctual Hilbert scheme is called curvilinear if it sits in the germ of a smooth curve on X. The irreducible component of the punctual Hilbert scheme containing these points is called the curvilinear component. We give a description of the curvilinear Hilbert scheme as a projective completion of the non-reductive quotient of holomorphic map germs from the complex line into X by holomorphic polynomial reparametrisations. Using an algebraic model of this quotient and equivariant localisation we develop an iterated residue formula for tautological integrals over the curvilinear component. We discuss possible generalisations for other non-reductive moduli problems.
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