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arXiv · 2501.00809

Initial ideals of weighted forms and the genus of locally Cohen-Macaulay curves

Alessio Sammartano·Enrico Schlesinger
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Abstract

Let C be a locally Cohen-Macaulay curve in complex projective 3-space. The maximum genus problem predicts the largest possible arithmetic genus g(d,s) that C can achieve assuming that it has degree d and does not lie on surfaces of degree less than s. In this paper, we prove that this prediction is correct when d=s or d is at least 2s-1. We obtain this result by proving another conjecture, by Beorchia, Lella, and the second author, about initial ideals associated to certain homogeneous forms in a non-standard graded polynomial ring.

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Alessio Sammartano, Enrico Schlesinger. 2025-01-01. Initial ideals of weighted forms and the genus of locally Cohen-Macaulay curves. https://doi.org/10.1007/s00209-026-03946-4

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