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Remark on the construction of the moduli space of semistable sheaves on the projective plane. (À propos de la construction de l’espace de modules des faisceaux semi- stables sur le plan projectif.) (French) Zbl 0829.14004
The author gives a construction of the \(S\)-equivalence classes of semi- stable sheaves on the plane proceeding directly from Kronecker complexes. The construction avoids Hilbert schemes and obtains the moduli space as the quotient of an open subset of a product of Grassmannians.

MSC:
14D22 Fine and coarse moduli spaces
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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References:
[1] DREZET (J.M.) et LE POTIER (J.) . - Fibrés stables et fibrés exceptionnels sur le plan projectif , Ann. Sci. École Norm. Sup. (4), t. 18, 1985 , p. 193-244. Numdam | MR 87e:14014 | Zbl 0586.14007 · Zbl 0586.14007
[2] ELLINGSRUD (G.) and STRØMME (S.A.) . - Towards the Chow ring of the Hilbert scheme of P2 , Preprint, 1992 .
[3] LE POTIER (J.) . - Fibrés vectoriels sur les courbes algébriques , cours de DEA, Université Paris 7, 1991 . MR 97c:14034
[4] MARUYAMA (M.) . - Moduli of stable sheaves , II, J. Math. Kyoto Univ., t. 18, 1978 , p. 557-614. Article | MR 82h:14011 | Zbl 0395.14006 · Zbl 0395.14006
[5] MUMFORD (D.) and FOGARTY (J.) . - Geometric Invariant Theory , Springer Verlag, 1982 . MR 86a:14006 | Zbl 0504.14008 · Zbl 0504.14008
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