Semantic Scholar Open Access 2000 63 sitasi

Derived Hilbert schemes

I. Ciocan-Fontanine Mikhail Kapranov

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (2)

I. Ciocan-Fontanine

Mikhail Kapranov

Format Sitasi

APA MLA BibTeX

Ciocan-Fontanine, I., Kapranov, M. (2000). Derived Hilbert schemes. https://doi.org/10.1090/S0894-0347-02-00399-5

Akses Cepat

Lihat di Sumber doi.org/10.1090/S0894-0347-02-00399-5

Informasi Jurnal

Tahun Terbit: 2000
Bahasa: en
Total Sitasi: 63×
Sumber Database: Semantic Scholar
DOI: 10.1090/S0894-0347-02-00399-5
Akses: Open Access ✓