Initial ideals of weighted forms and the genus of locally Cohen-Macaulay curves
| Autor: | Sammartano, Alessio, Schlesinger, Enrico |
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| Rok vydání: | 2025 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 49 pages, 6 figures. Comments are welcome! |
| Databáze: | arXiv |
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