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- W2046334625 abstract "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 Moreno-Socias conjecture implies Fr{o}berg conjecture. And for the case $Codim I le 3$, we show that $R/I$ has the strong Lefschetz property if and only if $gin(I)$ is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that $gin(I)$ is almost reverse lexicographic if $d_i > sum_{j=1}^{i-1} d_j - i + 1$ for each $i ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr{o}berg conjecture." @default.
- W2046334625 created "2016-06-24" @default.
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- W2046334625 date "2007-07-10" @default.
- W2046334625 modified "2023-09-23" @default.
- W2046334625 title "Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic" @default.
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