Secant functions, the Reiss relation and its converse
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- by Mark L. Green PDF
- Trans. Amer. Math. Soc. 280 (1983), 499-507 Request permission
Abstract:
Generalizing a classical Euclidean theorem for the circle, certain meromorphic functions on ${{\mathbf {P}}_1}$ relating to the geometry of algebraic plane curves are shown to be constant. Differentiated twice, this gives a new proof of the Reiss relation and its converse. The relation of these functions to Abel’s Theorem is discussed, and a generalization of secant functions to space curves is given, for which the Chow form arises in a natural way.References
- Mark L. Green and Ian Morrison, The equations defining Chow varieties, Duke Math. J. 53 (1986), no. 3, 733–747. MR 860668, DOI 10.1215/S0012-7094-86-05339-1
- Phillip A. Griffiths, Variations on a theorem of Abel, Invent. Math. 35 (1976), 321–390. MR 435074, DOI 10.1007/BF01390145
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 280 (1983), 499-507
- MSC: Primary 14N05; Secondary 14C17, 53A20
- DOI: https://doi.org/10.1090/S0002-9947-1983-0716834-4
- MathSciNet review: 716834