Geodesic
Monads of Stable Non-bundles on $\mathbb P^2$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 154-157.

Voir la notice de l'article provenant de la source Math-Net.Ru

The property of a semistable sheaf on the projective plane to be non-locally-free is translated to the language of linear algebra. The main result states that such a sheaf is characterized by the existence of some special subcomplex in the Beilinson–Gorodentsev monad. 
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B. V. Karpov. Monads of Stable Non-bundles on $\mathbb P^2$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 154-157. http://geodesic.mathdoc.fr/item/TM_2004_246_a10/

[1] Beilinson A. A., “Kogerentnye puchki na $\mathbb{P}^n$ i problemy lineinoi algebry”, Funkts. analiz i ego pril., 12:3 (1978), 68–69 | MR | Zbl

[2] Gorodentsev A. L., “Isklyuchitelnye rassloeniya na poverkhnostyakh s podvizhnym antikanonicheskim klassom”, Izv. AN SSSR. Ser. mat., 52:4 (1988), 740–757 | MR

[3] Kuleshov S. A., Moduli spaces of sheaves necessary for testing $S$-duality conjecture, Preprint MPI 97-32, Max-Planck-Inst., Bonn, 1997

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