摘要 : Let I be a homogeneous Artinian ideal in a polynomial ring R = k[x(1),..., x(n)] over a field k of characteristic 0. We study an equivalent condition for the generic initial ideal gin(I) with respect to reverse lexicographic order... 展开 Let I be a homogeneous Artinian ideal in a polynomial ring R = k[x(1),..., x(n)] over a field k of characteristic 0. We study an equivalent condition for the generic initial ideal gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that the Moreno-Socias conjecture implies the Froberg conjecture and the Pardue conjecture. And for the case codim 1 <= 3, we show that R/I has the strong Lefschetz property if and only if gin(I) is almost reverse lexicographic. Finally we give a positive partial answer to the Moreno-Socias conjecture, and hence to the Pardue conjecture. (C) 2008 Elsevier Inc. All rights reserved. 收起