Geodesic
Reducibility of the Moduli Space of Stable Rank $2$ Reflexive Sheaves with Chern Classes $c_1=-1$, $c_2=4$, $c_3=2$ on Projective Space $\mathbb{P}^3$
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 2, pp. 90-96.

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We prove the reducibility of the moduli space $M_{\mathbb{P}^3}^{\mathrm{ref}}(2;-1,4,2)$ of stable rank 2 reflexive sheaves with Chern classes $c_1=-1$, $c_2=4$, $c_3=2$ on projective space $\mathbb {P}^3$. This gives the first example of a reducible space in the series of moduli spaces of stable rank 2 reflexive sheaves with Chern classes $c_1=-1$, $c_2=4$, $c_3=2m$, $m=1,2,3,4,5,6,8$. We find two components of the expected dimension 27 of this space and give their geometric description via the Serre construction.
Mots-clés : moduli space, Serre construction.
Keywords: stable reflexive sheaf 
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     title = {Reducibility of the {Moduli} {Space} of {Stable} {Rank} $2$ {Reflexive} {Sheaves} with {Chern} {Classes}  $c_1=-1$, $c_2=4$, $c_3=2$ on {Projective} {Space} $\mathbb{P}^3$},
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A. S. Tikhomirov; M. A. Zavodchikov. Reducibility of the Moduli Space of Stable Rank $2$ Reflexive Sheaves with Chern Classes  $c_1=-1$, $c_2=4$, $c_3=2$ on Projective Space $\mathbb{P}^3$. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 2, pp. 90-96. http://geodesic.mathdoc.fr/item/MAIS_2014_21_2_a7/

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