Geodesic
Stable sheave moduli of rank~$2$ with Chern classes $c_1=-1$, $c_2=2$, $c_3=0$ on $Q_3$
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 19-39

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In this paper we consider the scheme $M_Q(2;-1,2,0)$ of stable torsion free sheaves of rank $2$ with Chern classes $c_1=-1$, $c_2=2$, $c_3=0$ on a smooth $3$-dimensional projective quadric $Q$. The manifold $M_Q(-1,2)$ of moduli bundles of rank $2$ with Chern classes $c_1=-1$, $c_2=2$ on $Q$ was studied by Ottaviani and Szurek in 1994. In 2007 the author described the closure $M_Q(-1,2)$ in the scheme $M_Q(2;-1,2,0)$. In this paper we prove that in $M_Q(2;-1,2,0)$ there exists a unique irreducible component different from $\overline{M_Q(-1,2)}$ which is a rational variety of dimension $10$.
Mots-clés : compactification, moduli scheme, $3$-dimensional quadric.
Keywords: coherent torsion free sheave of rank $2$ 
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     author = {A. D. Uvarov},
     title = {Stable sheave moduli of rank~$2$ with {Chern} classes $c_1=-1$, $c_2=2$, $c_3=0$ on $Q_3$},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {19--39},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a1/}
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A. D. Uvarov. Stable sheave moduli of rank~$2$ with Chern classes $c_1=-1$, $c_2=2$, $c_3=0$ on $Q_3$. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 19-39. http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a1/