Foundations of a general theory of birational correspondences
Author:
Oscar Zariski
Journal:
Trans. Amer. Math. Soc. 53 (1943), 490-542
MSC:
Primary 14.0X
DOI:
https://doi.org/10.1090/S0002-9947-1943-0008468-9
MathSciNet review:
0008468
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References | Similar Articles | Additional Information
- Heinrich Grell, Beziehungen zwischen den Idealen verschiedener Ringe, Math. Ann. 97 (1927), no. 1, 490–523 (German). MR 1512373, DOI https://doi.org/10.1007/BF01447879 W. Krull, Idealtheorie, Ergebnisse der Mathematik und ihrer Grenzgebiete, IV 3. ---, Dimensionstheorie in Stellenringen, J. Reine Angew. Math., vol. 179 (1938).
- Saunders Mac Lane and O. F. G. Schilling, Zero-dimensional branches of rank one on algebraic varieties, Ann. of Math. (2) 40 (1939), 507–520. MR 158, DOI https://doi.org/10.2307/1968935 F. K. Schmidt, Über die Erhaltung der Kettensätze der Idealtheorie bei beliebigen endlichen Körpererweiterungen, Math. Zeit. vol. 41 (1936). B. L. van der Waerden, Algebraische Korrespondenzen und rationale Abbildungen, Math. Ann. vol. 110 (1934).
- Oscar Zariski, Some Results in the Arithmetic Theory of Algebraic Varieties, Amer. J. Math. 61 (1939), no. 2, 249–294. MR 1507376, DOI https://doi.org/10.2307/2371499 ---, The reduction of the singularities of an algebraic surface, Ann. of Math. vol. 40 (1939).
- Oscar Zariski, Algebraic varieties over ground fields of characteristic zero, Amer. J. Math. 62 (1940), 187–221. MR 611, DOI https://doi.org/10.2307/2371447
- Oscar Zariski, Pencils on an algebraic variety and a new proof of a theorem of Bertini, Trans. Amer. Math. Soc. 50 (1941), 48–70. MR 4241, DOI https://doi.org/10.1090/S0002-9947-1941-0004241-4
- Oscar Zariski, A simplified proof for the resolution of singularities of an algebraic surface, Ann. of Math. (2) 43 (1942), 583–593. MR 6851, DOI https://doi.org/10.2307/1968814
- Oscar Zariski, Normal varieties and birational correspondences, Bull. Amer. Math. Soc. 48 (1942), 402–413. MR 6451, DOI https://doi.org/10.1090/S0002-9904-1942-07685-3
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Article copyright:
© Copyright 1943
American Mathematical Society