Derived Hilbert schemes
| dc.creator | Ciocan-Fontanine, I. | |
| dc.creator | Kapranov, M. | |
| dc.date | 2000-05-16 | |
| dc.date.accessioned | 2026-07-07T04:35:17Z | |
| dc.date.available | 2026-07-07T04:35:17Z | |
| dc.description | We construct the derived version of the Hilbert scheme parametrizing subschemes in a given projective scheme X with given Hilbert polynomial h. This is a dg-manifold (smooth dg-scheme) RHilb_h(X) which carries a natural family of commutative (up to homotopy) dg-algebras, which over the usual Hilbert scheme is just given by truncations of the homogeneous coordinate rings of subschemes in X. In particular, RHilb_h(X) differs from RQuot_h(O_X), the derived Quot scheme constructed in our previous paper (math.AG/9905174) which carries only a family of A-infinity modules over the coordinate algebra of X. As an application, we construct the derived version of the moduli stack of stable maps of (variable) algebraic curves to a given projective variety Y, thus realizing the original suggestion of M. Kontsevich. | |
| dc.description | 37 pages, AMS-Tex | |
| dc.identifier | https://arxiv.org/abs/math/0005155 | |
| dc.identifier | http://arxiv.org/abs/math/0005155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59204 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Derived Hilbert schemes | |
| dc.type | text |