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

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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. 
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     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},
     publisher = {mathdoc},
     volume = {82},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a9/}
}
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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/