Secant functions, the Reiss relation and its converse

Author:
Mark L. Green

Journal:
Trans. Amer. Math. Soc. **280** (1983), 499-507

MSC:
Primary 14N05; Secondary 14C17, 53A20

MathSciNet review:
716834

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Abstract: Generalizing a classical Euclidean theorem for the circle, certain meromorphic functions on 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.

**[1]**Mark L. Green and Ian Morrison,*The equations defining Chow varieties*, Duke Math. J.**53**(1986), no. 3, 733–747. MR**860668**, 10.1215/S0012-7094-86-05339-1**[2]**Phillip A. Griffiths,*Variations on a theorem of Abel*, Invent. Math.**35**(1976), 321–390. MR**0435074****[3]**Phillip Griffiths and Joseph Harris,*Principles of algebraic geometry*, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR**507725**

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1983-0716834-4

Article copyright:
© Copyright 1983
American Mathematical Society