Vol. 90, No. 1, 1980

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Moiré phenomena in algebraic geometry: rational alternations in R2

Keith Milo Kendig

Vol. 90 (1980), No. 1, 105–124

This paper investigates rational alternations, principally in R2. Rational alternations in Rn generalize the polynomial alternations studied in the author’s Moiré Phenomena in Algebraic Geometry: Polynomial Alternations in Rn. Rational alternations, like polynomial alternations, have the spirit of diffraction gratings, but may possess singularities, where grating bands flow together. Both alternations carry with them more information than ordinary varieties. As in the polynomial case, the systems of varieties making up two rational alternations generate new systems of varieties under union (or dually, intersection), corresponding to systems of moiré fringes of various orders. This paper investigates density functions naturally associated with these fringes, and studies the behavior of the fringes at points of indeterminacy of the defining functions.

Mathematical Subject Classification 2000
Primary: 14G30, 14G30
Secondary: 78A45
Received: 9 May 1979
Published: 1 September 1980
Keith Milo Kendig