Geodesic
A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 756-769 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new compactification of the variety of moduli of stable vector 2-bundles with Chern classes $c_1$ and $c_2$ is constructed for the case in which the universal family of stable sheaves with given values of invariants is defined and there are no strictly semistable sheaves. The compactification is a subvariety in the Hilbert scheme of subschemes of a Grassmann manifold with fixed Hilbert polynomial; it is obtained from the variety of bundle moduli by adding points corresponding to locally free sheaves on surfaces which are modifications of the initial surface. Moreover, a morphism from the new compactification of the moduli space to its Gieseker–Maruyama compactification is constructed.
Mots-clés : compactification, moduli space
Keywords: projective surface, Gieseker stable vector bundle, stable sheaf, Hilbert scheme, universal scheme, Grassmann manifold. 
@article{MZM_2007_82_5_a9,
     author = {N. V. Timofeeva},
     title = {A {Compactification} of the {Moduli} {Variety} of {Stable} {Vector} {2-Bundles} on a {Surface} in the {Hilbert} {Scheme}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {756--769},
     year = {2007},
     volume = {82},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a9/}
}
TY  - JOUR
AU  - N. V. Timofeeva
TI  - A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme
JO  - Matematičeskie zametki
PY  - 2007
SP  - 756
EP  - 769
VL  - 82
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a9/
LA  - ru
ID  - MZM_2007_82_5_a9
ER  - 
%0 Journal Article
%A N. V. Timofeeva
%T A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme
%J Matematičeskie zametki
%D 2007
%P 756-769
%V 82
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a9/
%G ru
%F MZM_2007_82_5_a9
N. V. Timofeeva. A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 756-769. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a9/

[1] D. Gieseker, “On the moduli of vector bundles on an algebraic surface”, Ann. of Math. (2), 106:1 (1977), 45–60 | DOI | MR | Zbl

[2] D. Huybrechts, M. Lehn, Geometry of Moduli Spaces of Sheaves, Aspects of Mathematics, E31, Vieweg, Braunschweig, 1997 | MR | Zbl

[3] H. Hironaka, “Resolution of singularities of an algebraic variety over a field of characteristic zero. I.”, Ann. of Math. (2), 79:1 (1964), 109–203 | DOI | MR | Zbl

[4] A. S. Tikhomirov, “Mnogoobrazie polnykh par nulmernykh podskhem algebraicheskoi poverkhnosti”, Izv. RAN. Ser. matem., 61:6 (1997), 153–180 | MR | Zbl

[5] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[6] R. Lazarsfeld, Positivity in Algebraic Geometry. I., Classical setting: line bundles and linear series, Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge A Series of Modern Surveys in Mathematics, 48, Springer-Verlag, Berlin, 2004 | MR | Zbl

[7] U. Fulton, Teoriya peresechenii, Mir, M., 1989 | MR | Zbl

[8] R. Godeman, Algebraicheskaya topologiya i teoriya puchkov, IL, M., 1961 | MR | Zbl