A combinatorial description of finite O-sequences and aCM genera. (March 2016) - Cioffi, Francesca; Lella, Paolo; Marinari, Maria Grazia
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.