Geodesic
Projective bundles, monoidal transformations, and derived categories of coherent sheaves
Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 133-141.

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This paper studies derived categories of coherent sheaves on varieties that are obtained by projectivization of vector bundles and by monoidal transformations. Conditions for the existence of complete exceptional sets in such categories are derived; they give new examples of varieties on which exceptional sets exist. 
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D. O. Orlov. Projective bundles, monoidal transformations, and derived categories of coherent sheaves. Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 133-141. http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a5/

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

[2] Bondal A. I., “Predstavleniya assotsiativnykh algebr v kogerentnye puchki”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 25–44 | MR

[3] Bondal A. I., Kapranov M. M., “Predstavimye funktory, funktory Serra i perestroiki”, Izv. AN SSSR. Ser. matem., 53:6 (1989), 1183–1205 | MR

[4] Gelfand S. I., Manin Yu. I., Vvedenie v gomologicheskuyu algebru, Nauka, M., 1989 | MR | Zbl

[5] Gorodentsev A. L., “Perestroika isklyuchitelnykh rassloenii na $\mathbf{P}^n$”, Izv. AN SSSR. Ser. matem., 52:1 (1988), 3–15 | MR

[6] Gorodentsev A. L., Rudakov A. Y., “Exceptional vector bundles on proiective spaces”, Duke Math. J., 54:1 (1987), 115–130 | DOI | MR | Zbl

[7] Kapranov M. M., “Proizvodnaya kategoriya kogerentnykh puchkov na mnogoobraziyakh Grassmana”, Izv. AN SSSR. Ser. matem., 48:1 (1984), 192–202 | MR

[8] Kapranov M. M., “Proizvodnaya kategoriya kogerentnykh puchkov na kvadrike”, Funkts. analiz v ego prilozh., 20:2 (1986), 67 | MR | Zbl

[9] Kapranov M. M., “On the derive categories of coherent sheaves on some homegeneous spaces”, Invent Math., 1988, no. 2, 479–508 | DOI | MR | Zbl

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

[11] Rudakov A. N., “Isklyuchitelnye rassloeniya na kvadrike”, Izv. AN SSSR. Ser. matem., 52:4 (1988), 788–812 | Zbl

[12] Khartskhori R., Algebraicheskaya geometriya, Mir, M., 1981 | MR