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In this paper, we are interested in the generic initial ideals of singular projective curves with respect to the graded lexicographic order. Let C be a singular irreducible projective curve of degree d⩾5 with the arithmetic genus ρa(C) in Pr where r⩾3. If M(IC) is the regularity of the lexicographic generic initial ideal of IC in a polynomial ring k[x0,…,xr] then we prove that M(IC) is 1+(d−12)−ρa(C)...
For a given term order, the degree complexity of a projective scheme is defined by the maximal degree of the reduced Gröbner basis of its defining saturated ideal in generic coordinates (Bayer and Mumford, 1993). It is well known that the degree complexity with respect to the graded reverse lexicographic order is equal to the Castelnuovo–Mumford regularity (Bayer and Stillman, 1987). However, much...
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