Foundations of the theory of Fano schemes
Altman, Allen B. ; Kleiman, Steven L.
Compositio Mathematica, Tome 35 (1977), p. 3-47 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CM_1977__34_1_3_0,
     author = {Altman, Allen B. and Kleiman, Steven},
     title = {Foundations of the theory of Fano schemes},
     journal = {Compositio Mathematica},
     volume = {35},
     year = {1977},
     pages = {3-47},
     mrnumber = {569043},
     zbl = {0414.14024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1977__34_1_3_0}
}

Altman, Allen B.; Kleiman, Steven L. Foundations of the theory of Fano schemes. Compositio Mathematica, Tome 35 (1977) pp. 3-47. http://gdmltest.u-ga.fr/item/CM_1977__34_1_3_0/

[A] Artin, M.: Algebraization of formal moduli I. Global Analysis ("Kodaira volume"), edited by D. C. Spencer and S. Iyanaga, Princeton University Press (1969), 21-71. | MR 260746 | Zbl 0205.50402

[ASDS] Altman, A.B. and Kleiman, S.L.: Algebraic systems of linearly equivalent divisor-like subschemes. Comp. Math. 29 (1974) 113-139. | Numdam | MR 376668 | Zbl 0337.14009

[BC] Altman, A.B., Hoobler, R.T. and Kleiman, S.L.: A note on the base change map for cohomology, Comp. Math. 27 (1973) 25-38. | Numdam | MR 337971 | Zbl 0267.14001

[B, S-D] Bombieri, E. and Swinnerton-Dyer: On the local zeta function of a cubic threefold. Ann. Scuola Norm. Sup. Pisa (3) 27 (1967) 1-29. MR 35 #2894. | Numdam | MR 212019 | Zbl 0153.50501

[C, G] Clemens, C.H. and Griffiths, P.A.: The intermediate jacobian of the cubic threefold, Annals of Math. 95 (1972) 281-356. | MR 302652 | Zbl 0214.48302

[Ch] Grothendieck, A.: La théorie des classes de Chern. Bull. Soc. Math. France, 86 (1958) 137-154. | Numdam | MR 116023 | Zbl 0091.33201

[EGA I] Grothendieck, A. and Dieudonné, J.: Eléments de Géométrie Algébrique I. Springer-Verlag (1971). | Zbl 0203.23301

[EGA II]-[EGA IV4] Grothendieck, A. and Dieudonné, J.: Eléments de Géométrie Algébrique, Publ. Math. IHES 8, 11, 17, 20, 24, 28, 32 (1961, '61, '63, '64, '65, '66, '67). | Numdam

[F 1] Fano, G.: Sulle superficie algebriche contenute in una varietà cubica generate dello spazio a quattro dimensioni. Atti Reale Accad. Sci. Torino 39 (1904) 597-613. | JFM 35.0656.01

[F 2] Fano, G.: Sul sistema ∞2 di rette contenuto in una varietà cubica generale dello spacio a quattro dimensioni. Atti Reale Accad. Sci. Torino 38 (1904) 778-792. | JFM 35.0657.01

[FGA] Grothendieck, A.: Technique de descente et théorèmes d'existence en géométrie algébrique, IV: Les schémas de Hilbert. Séminaire Bourbaki, t. 14, Février 1962, no. 232, 19 pages. | Numdam | Zbl 0238.14014

[GD] Altman, A.B. and Kleiman, S.L.: Introduction to Grothendieck duality theory. Lecture notes in math. 146. Springer (1970). | MR 274461 | Zbl 0215.37201

[Gr 1] Griffiths, P.A.: Hermitian differential geometry, Chern classes, and positive vector bundles, Global Analysis ("Kodaira volume"), edited by D. C. Spencer and S. Iyanaga, Princeton University Press (1969), 185-251. | MR 258070 | Zbl 0201.24001

[Gr 2] Griffiths, P.A.: Periods of integrals on algebraic manifolds; summary of main results and discussion of open problems, Bull. A.M.S. 76 (1970) 228-296. MR 41 #3470. | MR 258824 | Zbl 0214.19802

[J] Altman, A.B. and Kleiman, S.L.: Joins of schemes, linear projections. Comp. Math. 31 (1975) 309-343. | Numdam | MR 396560 | Zbl 0337.14004

[K] Kempf, G.: The singularities of certain varieties in the jacobian of a curve. thesis, Columbia University, New York (Feb. 1971).

[Kl 1] Kleiman, S.L.: Geometry on grassmannians and applications to splitting bundles and smoothing cycles, Publ. Math. IHES 36 (1969) ("Zariski volume") 281-297. | Numdam | MR 265371 | Zbl 0208.48501

[Kl 2] Kleiman, S.L.: Problem 15. Rigorous foundation of Schubert's enumerative calculus, (to appear in an AMS volume on the Hilbert problems). | Zbl 0336.14001

[Lb] Lieberman, D., (personal communication).

[Lk]Laksov, D.: The arithmetic Cohen-Macaulay character of Schubert schemes. Acta Math. 129 (1972) 1-9. | MR 382297 | Zbl 0233.14012

[Lp] Lipman, J., (personal communication).

[Lr] Libgober, A.S.: Numerical characteristics of systems of straight lines on complete intersections. Math. Notes 13 (1973) 51-56. Translated from Matematicheskie Zametki 13 (1973) 87-96. | MR 332810 | Zbl 0264.14012

[M 1] Mumford, D.: Lectures on curves on an algebraic surface. Princeton University Press (1966). | MR 209285 | Zbl 0187.42701

[M 2] Mumford, D.: Abelian varieties. Tata Inst. Fund. Research, Bombay, and Oxford University Press (1970). | MR 282985 | Zbl 0223.14022

[Mr 1] Murre, J.P.: Algebraic equivalence modulo rational equivalence on a cubic threefold. Comp. Math. 25 (1972) 161-206. | Numdam | MR 352088 | Zbl 0242.14002

[Mr 2] Murre, J.P.: Reduction of the proof of the nonrationality of a nonsingular cubic threefold to a result of Mumford. Comp. Math. 27 (1973) 63-82. | Numdam | MR 352089 | Zbl 0271.14020

[P] Porteous, I.R.: Simple singularities of maps, Liverpool singularity symposium I. Lecture notes in math. 192. Springer (1971) 286-307. | MR 293646 | Zbl 0221.57016

[RD] Hartshorne, R.: Residues and duality. Lecture notes in math. 20. Springer (1966). | MR 222093 | Zbl 0212.26101

[S] Svanes, T., (personal communication).

[SGA 3] Demazure, M. and Grothendieck, A.: Schémas en Groupes I. Lecture notes in math. 151. Springer (1970). | MR 274458 | Zbl 0207.51401

[SGA 6] Berthelot, P., Grothendieck, A., Illusie, L.: Théorie des intersections et théorème de Riemann-Roch. Séminaire de géométrie algébrique du Bois Marie 1966/67. Lecture notes in math. 225. Springer (1971). | MR 354655 | Zbl 0218.14001

[Tj 1] Tjurin, A.N.: On the Fano surface of a nonsingular cubic in P4. Izv. Akad. Nauk. SSSR Ser. Mat. 34 (1970) 1200-1208= Math. USSR Izv. 4 (1970) 1207-1214. | MR 277541 | Zbl 0225.14019

[Tj 2] Tjurin, A.N.: The geometry of the Fano surface of a nonsingular cubic F ⊂ P4 and Torelli theorems for Fano surfaces and cubics. Izv. Akad. Nauk SSSR. Ser. Mat. 35 (1971) 458-529= Math. USSR Izv. 5 (1971) 517-546. | Zbl 0252.14004

[Tn] Tennison, B.R.: On the quartic threefold. P. Lond. Math. Soc. XXIX (1974) 714-734. | MR 419453 | Zbl 0308.14005