Abstract
It is not known whether Macaulay's curve is a set-theoretic complete intersection or not in characteristic zero. There are known (weak) indications that the answer is negative; clearly, a negative such answer would provide the first example of an irreducible non-set-theoretic complete intersection curve, i.e., of a curve in affine or projective n-space that cannot be cut out by n − 1 polynomial equations.We prove new necessary conditions for two (assumed) homogeneous polynomials cutting out C4 set-theoretically. We use local cohomology and an idea from Thoma.
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