Varieties of small codimension in projective space

Hartshorne, Robin

doi:10.1090/S0002-9904-1974-13612-8

Varieties of small codimension in projective space
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Bull. Amer. Math. Soc. 80 (1974), 1017-1032

References

Aldo Andreotti and Theodore Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. (2) 69 (1959), 713–717. MR 177422, DOI 10.2307/1970034
M. F. Atiyah and F. Hirzebruch, Analytic cycles on complex manifolds, Topology 1 (1962), 25–45. MR 145560, DOI 10.1016/0040-9383(62)90094-0
W. Barth, Transplanting cohomology classes in complex-projective space, Amer. J. Math. 92 (1970), 951–967. MR 287032, DOI 10.2307/2373404
W. Barth and M. E. Larsen, On the homotopy groups of complex projective algebraic manifolds, Math. Scand. 30 (1972), 88–94. MR 340643, DOI 10.7146/math.scand.a-11066
W. Barth and A. Van de Ven, A decomposability criterion for algebraic $2$-bundles on projective spaces, Invent. Math. 25 (1974), 91–106. MR 379515, DOI 10.1007/BF01389999
Raoul Bott, On a theorem of Lefschetz, Michigan Math. J. 6 (1959), 211–216. MR 215323
Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307 (French). MR 340258
A. Grothendieck, Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math. 79 (1957), 121–138 (French). MR 87176, DOI 10.2307/2372388
Alexander Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux $(SGA$ $2)$, North-Holland Publishing Co., Amsterdam; Masson & Cie, Editeur, Paris, 1968 (French). Augmenté d’un exposé par Michèle Raynaud; Séminaire de Géométrie Algébrique du Bois-Marie, 1962; Advanced Studies in Pure Mathematics, Vol. 2. MR 0476737
Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977
Robin Hartshorne, Cohomology of non-complete algebraic varieties, Compositio Math. 23 (1971), 257–264. MR 302649
Robin Hartshorne and Arthur Ogus, On the factoriality of local rings of small embedding codimension, Comm. Algebra 1 (1974), 415–437. MR 347821, DOI 10.1080/00927877408548627
Robin Hartshorne, Elmer Rees, and Emery Thomas, Nonsmoothing of algebraic cycles on Grassmann varieties, Bull. Amer. Math. Soc. 80 (1974), 847–851. MR 357402, DOI 10.1090/S0002-9904-1974-13537-8
Robin Hartshorne and Robert Speiser, Local cohomological dimension in characteristic $p$, Ann. of Math. (2) 105 (1977), no. 1, 45–79. MR 441962, DOI 10.2307/1971025
Heisuke Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math. 90 (1968), 1–54. MR 224611, DOI 10.2307/2373425
F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
W. V. D. Hodge, The topological invariants of algebraic varieties, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 1, Amer. Math. Soc., Providence, R.I., 1952, pp. 182–192. MR 0046075
G. Horrocks, A construction for locally free sheaves, Topology 7 (1968), 117–120. MR 227180, DOI 10.1016/0040-9383(68)90018-9
G. Horrocks and D. Mumford, A rank $2$ vector bundle on $\textbf {P}^{4}$ with $15,000$ symmetries, Topology 12 (1973), 63–81. MR 382279, DOI 10.1016/0040-9383(73)90022-0
Steven L. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 281–297. MR 265371
Mogens Esrom Larsen, On the topology of complex projective manifolds, Invent. Math. 19 (1973), 251–260. MR 318511, DOI 10.1007/BF01390209
Solomon Lefschetz, On certain numerical invariants of algebraic varieties with application to abelian varieties, Trans. Amer. Math. Soc. 22 (1921), no. 3, 327–406. MR 1501178, DOI 10.1090/S0002-9947-1921-1501178-3
Emilio Lluis, Sur l’immersion des variétés algébriques, Ann. of Math. (2) 62 (1955), 120–127 (French). MR 71112, DOI 10.2307/2007102
Masaki Maruyama, On a family of algebraic vector bundles, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 95–146. MR 0360587
Masayoshi Nagata, Existence theorems for nonprojective complete algebraic varieties, Illinois J. Math. 2 (1958), 490–498. MR 97406
Arthur Ogus, Local cohomological dimension of algebraic varieties, Ann. of Math. (2) 98 (1973), 327–365. MR 506248, DOI 10.2307/1970785
C. Peskine and L. Szpiro, Liaison des variétés algébriques. I, Invent. Math. 26 (1974), 271–302 (French). MR 364271, DOI 10.1007/BF01425554
Joel Roberts, Generic projections of algebraic varieties, Amer. J. Math. 93 (1971), 191–214. MR 277530, DOI 10.2307/2373457
Pierre Samuel, Méthodes d’algèbre abstraite en géométrie algébrique, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 4, Springer-Verlag, Berlin-New York, 1967 (French). Seconde édition, corrigée. MR 0213347
J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Oxford, at the Clarendon Press, 1949. MR 0034048
H. P. F. Swinnerton-Dyer, An enumeration of all varieties of degree $4$, Amer. J. Math. 95 (1973), 403–418. MR 340253, DOI 10.2307/2373791
L. Szpiro, Variétés de codimension 2 dans $\textbf {P}^{n}$, Colloque d’Algèbre Commutative (Rennes, 1972) Publ. Sém. Math. Univ. Rennes, Année 1972, Univ. Rennes, Rennes, 1972, pp. 7 (French). MR 0463186
André Weil, Introduction à l’étude des variétés kählériennes, Publications de l’Institut de Mathématique de l’Université de Nancago, VI. Actualités Sci. Ind. no. 1267, Hermann, Paris, 1958 (French). MR 0111056
Correspondence, Amer. J. Math. 79 (1957), 951–952. Attributed to A. Weil. MR 123574, DOI 10.2307/2372446