zbMATH — the first resource for mathematics

The Castelnuovo criterion of rationality. (English) Zbl 0237.14020
14M20 Rational and unirational varieties
Full Text: DOI
[1] M. Artin, ?The etal topology of schemes,? in: Proceedings of the International Congress of Mathematicians (in Moscow, 1966) [in Russian], Moscow (1968), pp. 44-56.
[2] M. Artin and A. Grothendieck, SGAA (1963-1964).
[3] A. Borel and J.-P Serre, ?Le théoréme de Reimann-Roch,? Bull. Soc. Math. France,86, No. 2, 7-136 (1958).
[4] A. Grothendieck, ?Formule de Lefschetz et rationalité des fonctions L,? Sem. Bourbaki, No. 279 (1964/65); ?Le groupe de Brauer. I, II,? Nos. 290, 297 (1964/65).
[5] J. I. Igusa, ?Betti and Picard numbers of abstract algebraic surfaces,? Proc. Nat. Acad. Sci.,46, 724-726 (1960). · Zbl 0099.16402 · doi:10.1073/pnas.46.5.724
[6] Algebraic Surfaces [in Russian], ed. I. R. Shafarevich, Trudy Matem. In-ta Akad. Nauk SSSR, Moscow (1965).
[7] J.-P. Serre, Sem. Bourbaki, Exp. 146 (1957).
[8] J.-P Serre, Cohomologie Galoisienne, Lecture Notes in Math., No. 5, New York (1964).
[9] J. Tate, ?Genus change in inseparable extensions of function fields,? Proc. Amer. Math. Soc.,3, 400-406 (1952). · Zbl 0047.03901 · doi:10.1090/S0002-9939-1952-0047631-9
[10] O. Zariski, ?The problem of minimal models in the theory of algebraic surfaces,? Amer. J. of Math.,80, 146-183 (1958). · Zbl 0085.36202 · doi:10.2307/2372827
[11] O. Zariski, ?On Castelnuovo’s criterion of rationality in the theory of algebraic surfaces,? Illinois J. of Math.,2, 303-315 (1958). · Zbl 0085.36203
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.