- #1
naturemath
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Doesn't a linear change of coordinates preserve complete intersection for a set of homogeneous polynomials, all of the same degree, in a polynomial ring?
That is, apply a change of coordinates to a set of homogeneous polynomials {f_1,... f_k} in C[x_1,...,x_M] to obtain {h_1,..., h_k}. Suppose now that the variety cut out by {h_1,...,h_k} is a complete intersection. Doesn't this imply that the original set of generators {f_1,... f_k} formed a complete intersection?
This seems very plausible.
That is, apply a change of coordinates to a set of homogeneous polynomials {f_1,... f_k} in C[x_1,...,x_M] to obtain {h_1,..., h_k}. Suppose now that the variety cut out by {h_1,...,h_k} is a complete intersection. Doesn't this imply that the original set of generators {f_1,... f_k} formed a complete intersection?
This seems very plausible.
