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Transactions of the American Mathematical Society

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Hilbert's characteristic function and the arithmetic genus of an algebraic variety


Authors: H. T. Muhly and O. Zariski
Journal: Trans. Amer. Math. Soc. 69 (1950), 78-88
MSC: Primary 14.0X
DOI: https://doi.org/10.1090/S0002-9947-1950-0037547-9
MathSciNet review: 0037547
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  • [1] B. L. van der Waerden, On Hilbert's function, series of composition of ideals, and a generalization of a theorem of Bezout, Proceedings of the Koninklijke Akademie van Wetenschappen, Amsterdam vol. 31 (1928).
  • [2] O. Zariski, The reduction of the singularities of an algebraic surface, Ann. of Math. vol. 40 (1939).
  • [3] -, A simplified proof of the resolution of singularities of an algebraic surface, Ann. of Math. vol. 43 (1942). MR 0006851 (4:52c)
  • [4] -, Pencils on an algebraic variety and a new proof of a theorem of Bertini, Trans. Amer. Math. Soc. vol. 50 (1941). MR 0004241 (2:345a)
  • [5] -, Foundations of a general theory of birational correspondences, Trans. Amer. Math. Soc. vol. 53 (1943). MR 0008468 (5:11b)
  • [6] -, The theorem of Bertini on the variable singular points of a linear system of varieties, Trans. Amer. Math. Soc. vol. 56 (1944). MR 0011572 (6:186a)
  • [7] -, Reduction of the singularities of algebraic three dimensional varieties, Ann. of Math. vol. 45 (1944). MR 0011006 (6:102f)

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DOI: https://doi.org/10.1090/S0002-9947-1950-0037547-9
Article copyright: © Copyright 1950 American Mathematical Society

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