Geodesic
Some new components of the moduli scheme $\mathrm M_{\mathbb P^3}(2;-1,2,0)$ of stable coherent torsion free sheaves of rank~2 on $\mathbb P^3$
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 5-18.

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In this paper we consider Giseker–Maruyama moduli scheme $\mathrm M:=\mathrm M_{\mathbb P^3}(2;-1,2,0)$ of stable coherent torsion free sheaves of rank 2 with Chern classes $c_1=-1$, $c_2=2$, $c_3=0$ on 3-dimensional projective space $\mathbb P ^3$. We will define two sets of sheaves $\mathcal M_1$ and $\mathcal M_2$ in $\mathrm M$ and we will prove that closures of $\mathcal M_1$ and $\mathcal M_2$ in $\mathrm M$ are irreducible components of dimensions 15 and 19, accordingly.
Mots-clés : compactification, moduli scheme
Keywords: coherent torsion free sheave of rank 2, 3-dimensional projective space. 
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M. A. Zavodсhikov. Some new components of the moduli scheme  $\mathrm M_{\mathbb P^3}(2;-1,2,0)$  of stable coherent torsion free sheaves of rank~2 on $\mathbb P^3$. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 5-18. http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a0/

[1] K. Okonek, M. Shneider, Kh. Shpindler, Vektornye rassloeniya na kompleksnykh proektivnykh prostranstvakh, Mir, M., 1984 | MR | Zbl

[2] R. Hartshorne, I. Sols, “Stable rank 2 vector bundles on $\mathbb{P}^3$ with $c_1=-1, c_2=2$”, J. Reine Angew. Math., 325 (1981), 145–152 (English) | MR | Zbl

[3] J. Meseguer, I. Sols, S. A. Stromme, “Compactification of a family of vector bundles on $\mathbb{P}\sp 3$”, Prog. Math., 18th Scand. Congr. Math., Proc. (Aarhus 1980), v. 11, 1981, 474–494 (English) | MR | Zbl

[4] R. Hartshorne, “Stable reflexive sheaves”, Math. Ann., 254 (1980), 121–176 (English) | DOI | MR | Zbl

[5] D. Huyberchts, M. Lehn, The Geometry of moduli spaces of sheaves, A Publication of the Max-Planck-Institut für Matematik, Bonn, 1997

[6] M.-C. Chang, “Stable rank $2$ reflexive sheaves on $\mathbb P^3$ with small $c_2$ and applications”, Trans. Amer. Math. Soc., 284:1 (1984), 57–89 | MR | Zbl

[7] M. Maruyama, “Moduli of stable sheaves. II”, J. Math. Kyoto Univ., 18 (1978), 557–614 (English) | MR | Zbl

[8] S.-A. Stromme, “Ample Divisors on Fine Moduli Spaces on Projective Plane”, Math. Z., 187 (1984), 405–423 | DOI | MR