A combinatorial description of finite O-sequences and aCM genera. (March 2016)

• Record Type: Journal Article
• Authors: Cioffi, Francesca; Lella, Paolo; Marinari, Maria Grazia
• Is Part Of: Journal of symbolic computation. Volume 73(2016)
• Page Start: 104
• Page End: 119
• Publication Date: 2016-03
• Subjects: 13C14 -- 14N10 -- 14H99 -- 14Q05 -- 05C20; aCM genus -- Finite O-sequence -- Cohen–Macaulay curve -- Directed graph -- Partial order; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.03.006
• Languages: English
• ISSNs: 0747-7171

Abstract

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 { 0, …, ( d − 1 2 ) } . 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.