Generic initial ideals of singular curves in graded lexicographic order

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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 rho(a)(C) in P-r where r >= 3. If M(I-C) is the regularity of the lexicographic generic initial ideal of I-C in a polynomial ring k[chi(0,) . . . . chi(r)] then we prove that M(I-C) is 1 + ((d-1)(2)) - rho(a)(C) which is obtained from the monomial [GRAPHICS] provided that dim Tan(p)(C) = 2 for every singular point p is an element of C. This number is equal to one plus the number of secant lines through the center of general projection into P-2. Our result generalizes the work of J. Ahn (2008) [1] for smooth projective curves and that of A. Conca and J. Sidman (2005) [9] for smooth complete intersection curves in P-3. The case of singular curves was motivated by A. Conca and J. Sidman (2005) [9, Example 4.3]. We also provide some illuminating examples of our results via calculations done with Macaulay 2 and singular (Decker et al., 2011 [10], Grayson and Stillman [16]). (C) 2012 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2012-12
Language
English
Article Type
Article
Keywords

CASTELNUOVO-MUMFORD REGULARITY; DEGREE-COMPLEXITY; SMOOTH SURFACES; CODIMENSION 2; THREEFOLDS

Citation

JOURNAL OF ALGEBRA, v.372, pp.584 - 594

ISSN
0021-8693
DOI
10.1016/j.jalgebra.2012.09.011
URI
http://hdl.handle.net/10203/104405
Appears in Collection
MA-Journal Papers(저널논문)
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