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Original Articles

Bundles over the Fano Threefold V5

Pages 3061-3080 | Received 27 Apr 2004, Published online: 21 Oct 2011

REFERENCES

  • Aluffi , P. , Faber , C. ( 1993 ). Linear orbits of d-tuples of points in P 1 . J. Reine Angew. Math. 445 : 205 – 220 . MR 94j:14044 [CSA]
  • Ancona , V. , Ottaviani , G. ( 1991 ). Some applications of Beilinson's theorem to projective spaces and quadrics . Forum Math. 3 ( 2 ): 157 – 176 . MR 92e:14039 [CSA]
  • Arrondo , E. , Costa , L. ( 2000 ). Vector bundles on Fano 3-folds without intermediate cohomology . Comm. Algebra 28 ( 8 ): 3899 – 3911 . MR 2001d:14043 [CSA]
  • Arrondo , E. , Graña , B. ( 1999 ). Vector bundles on G(1, 4) without intermediate cohomology . J. Algebra 214 ( 1 ): 128 – 142 . MR 2000e:14069 [CROSSREF] [CSA]
  • Beilinson , A. A. ( 1978 ). Coherent sheaves on P n and problems in linear algebra . Funktsional. Anal. i Prilozhen. 12 ( 3 ): 68 – 69 . MR 80c:14010b [CSA]
  • Bondal , A. I. ( 1990 ). Helices, representations of quivers and Koszul algebras . Helices and Vector Bundles . London Math. Soc. Lecture Note Ser. , Vol. 148 . Cambridge : Cambridge Univ. Press , pp. 75 – 95 . MR 92i:14016
  • Buchsbaum , D. A. , Eisenbud , D. ( 1977 ). Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3 . Amer. J. Math. 99 ( 3 ): 447 – 485 . MR 56 #11983 [CSA]
  • Canonaco , A. ( 2000 ). A Beilinson-type theorem for coherent sheaves on weighted projective spaces . J. Algebra 225 ( 1 ): 28 – 46 . MR 2001g:14019 [CROSSREF] [CSA]
  • Castelnuovo , G. (1891). Ricerche di geometria della retta nello spazio a quattro dimensioni. Atti del R. Ist. Veneto di Scienze, Lettere e Arti 7(2):855–901. [CSA]
  • Drezet , J.-M. ( 1986 ). Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur P 2(C) . Math. Ann. 275 ( 1 ): 25 – 48 . MR 88b:14014 [CROSSREF] [CSA]
  • Drezet , J.-M. ( 1988 ). Cohomologie des variétés de modules de hauteur nulle . Math. Ann. 281 ( 1 ): 43 – 85 . MR 89j:14009 [CROSSREF] [CSA]
  • Gelfand , S. I. , Manin , Y. I. ( 1996 ). ethods of Homological Algebra . Berlin : Springer-Verlag . Translated from the 1988 Russian original. MR 97j:18001
  • Gorodentsev , A. L. ( 1990 ). Exceptional objects and mutations in derived categories . Helices and Vector Bundles . London Math. Soc. Lecture Note Ser. , Vol. 148 . Cambridge Univ. Press , Cambridge , pp. 57 – 73 . MR 91m:14024
  • Horrocks , G. ( 1964 ). Vector bundles on the punctured spectrum of a local ring . Proc. London Math. Soc. (3) 14 : 689 – 713 . MR 30 #120 [CSA]
  • Huybrechts , D. , Lehn , M. ( 1997 ). The geometry of moduli spaces of sheaves . Aspects of Mathematics Braunschweig: E31, Friedr. Vieweg & Sohn. MR 98g:14012 [CSA]
  • Iskovskih , V. A. ( 1977 ). Fano threefolds. I . Izv. Akad. Nauk SSSR Ser. Mat. 41 ( 3 ): 516 – 562 , 717. MR 80c:14023a. English translation: part I, Math. USSR = Izv. 11 (1977), no. 3, 485–527 (1978); part II, ibid. 12 (1978), no. 3, 469–506 (1979) . [CSA]
  • Iskovskih , V. A. ( 1978 ). Fano threefolds. II . Izv. Akad. Nauk SSSR Ser. Mat. 42 ( 3 ): 506 – 549 . MR 80c:14023b [CSA]
  • Iskovskikh , V. A. , Prokhorov , Y. G. ( 1999 ). Fano varieties . Algebraic Geometry, V . Encyclopaedia Math. Sci. Vol. 47 . Berlin : Springer , pp. 1 – 247 . MR 2000b:14051b
  • Kapranov , M. M. ( 1988 ). On the derived categories of coherent sheaves on some homogeneous spaces . Invent. Math. 92 ( 3 ): 479 – 508 . MR 89g:18018 [CROSSREF] [CSA]
  • Kawamata , Y. ( 2002 ). Equivalences of derived categories of sheaves on smooth stacks . http://arXiv.org/abs/math.AG/0210439 . Amer. J. Math. 126 ( 2004 ), no. 5 , 1057 – 1083 . [CSA]
  • Maruyama , M. ( 1981 ). The theorem of Grauert-Mülich-Spindler . Math. Ann. 255 ( 3 ): 317 – 333 . MR 82k:14012 [CROSSREF] [CSA]
  • Mukai , S. ( 1988 ). Curves, K3 surfaces and Fano 3-folds of genus ≤10 . Algebraic Geometry and Commutative Algebra . Vol. I . Tokyo : Kinokuniya , pp. 357 – 377 . MR 90b:14039
  • Mukai , S. ( 1992 ). Fano 3-folds. Complex Projective Geometry (Trieste, 1989/Bergen, 1989). London Math. Soc. Lecture Note Ser. , Vol. 179 . Cambridge : Cambridge Univ. Press , pp. 255 – 263 . MR 94a:14042
  • Mukai , S. , Umemura , H. ( 1983 ). Minimal rational threefolds . Algebraic Geometry (Tokyo/Kyoto, 1982) . Lecture Notes in Math. , Vol. 1016 . Berlin : Springer , pp. 490 – 518 . MR 85c:14027
  • Nogin , D. Y. ( 1994 ). Helices on some Fano threefolds: constructivity of semiorthogonal bases of K 0 . Ann. Sci. École Norm. Sup. (4) 27 ( 2 ): 129 – 172 . MR 95e:14030 [CSA]
  • Orlov , D. O. ( 1991 ). Exceptional set of vector bundles on the variety V 5 . Vestnik Moskov. Univ. Ser. I Mat. Mekh. ( 5 ): 69 – 71 . MR 95f:14080. Vestnik Moskov. Univ. Ser. I Math. Mekh. (1989), no. 2, 43–47, 105; translation in Moscow Univ. Math. Bull. 44 (1989), no. 2, 65–69 . [CSA]
  • Ottaviani , G. ( 1989 ). Some extensions of Horrocks criterion to vector bundles on Grassmannians and quadrics . Ann. Mat. Pura Appl. (4) 155 : 317 – 341 . MR 91f:14018 [CROSSREF] [CSA]
  • Rudakov , A. N. ( 1990 ). Exceptional collections, mutations and helices . Helices and Vector Bundles . London Math. Soc. Lecture Note Ser. , Vol. 148 . Cambridge : Cambridge Univeristy Press , pp. 1 – 6 . MR 93a:14016. English translation: Functional Anal. Appl. 12 (1978), no. 3, 212–214 (1979); ibid. 12 (1978), no. 3, 214–216 (1979) .
  • # Communicated by R. Piene.

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