Geodesic
A four-dimensional bundle of quadrics, and a~monad
Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 207-220.

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In this paper the author constructs a regular mapping $f$ of the variety of moduli of stable two-dimensional vector bundles $\mathscr F$ on $P^3$ with Chern classes $c_1(\mathscr F)=0$ and $c_2(\mathscr F)=n$ which satisfy $h^1(P^3,\mathscr F(-2))=0$, into the variety of classes of four-dimensional bundles of quadrics (whose base is the Grassmannian $G(1,3)$) in $P^{n-1}$. He proves that $f$ is an embedding. For the proof he constructs a monad on $P^3$ for the class of $f(\mathscr F)$, such that the cohomology sheaf of the monad is isomorphic to the vector bundle $\mathscr F$. Bibliography: 4 titles. 
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A. S. Tikhomirov. A four-dimensional bundle of quadrics, and a~monad. Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 207-220. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a10/

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[2] Barth W., Hulek K., “Monads and moduli of vector bundles”, Manuscripta math., 25 (1978), 323–347 | DOI | MR | Zbl

[3] Barth W., “Moduli of stable vector bundles on the projective plane”, Inventiones math., 42 (1977), 63–91 | DOI | MR | Zbl

[4] Barth W., “Some properties of stable rank-2 vector bundles on $P_n$”, Math. Ann., 226 (1977), 125–150 | DOI | MR | Zbl