The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen–Macaulay projective curves with a given degree d. It is well-known that the arithmetic genus g of a curve C can be easily deduced from the h-vector of the curve; in the case where C is arithmetically Cohen–Macaulay of degree d, g must belong to the range of integers . We develop an algorithmic procedure that allows one to avoid constructing most of the possible h-vectors of C. The essential tools are a combinatorial description of the finite O-sequences of multiplicity d, and a sort of continuity result regarding the generation of the genera. The efficiency of our method is supported by computational evidence. As a consequence, we single out the minimal possible Castelnuovo–Mumford regularity of a curve with Cohen–Macaulay postulation and given degree and genus. ©2015 Elsevier Ltd. All rights reserved.

A combinatorial description of finite O-sequences and aCM genera / Francesca, Cioffi; Lella, Paolo; Maria Grazia, Marinari. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 73:(2016), pp. 104-119. [10.1016/j.jsc.2015.03.006]

A combinatorial description of finite O-sequences and aCM genera

Lella, Paolo;
2016-01-01

Abstract

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen–Macaulay projective curves with a given degree d. It is well-known that the arithmetic genus g of a curve C can be easily deduced from the h-vector of the curve; in the case where C is arithmetically Cohen–Macaulay of degree d, g must belong to the range of integers . We develop an algorithmic procedure that allows one to avoid constructing most of the possible h-vectors of C. The essential tools are a combinatorial description of the finite O-sequences of multiplicity d, and a sort of continuity result regarding the generation of the genera. The efficiency of our method is supported by computational evidence. As a consequence, we single out the minimal possible Castelnuovo–Mumford regularity of a curve with Cohen–Macaulay postulation and given degree and genus. ©2015 Elsevier Ltd. All rights reserved.
2016
Francesca, Cioffi; Lella, Paolo; Maria Grazia, Marinari
A combinatorial description of finite O-sequences and aCM genera / Francesca, Cioffi; Lella, Paolo; Maria Grazia, Marinari. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 73:(2016), pp. 104-119. [10.1016/j.jsc.2015.03.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/106506
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