Abstract: Let $R = k[x_1, ..., x_p]$ and $I$ be a squarefree monomial ideal over $R$ with $g$ minimal generators. The projective dimension is the length of the minimal resolution of $I$, which sometimes depends on the characteristic of $k$. Given integers $n,i$ such that $g ≥ 3n - 1$ and $3 ≤ n ≤ i ≤ g - n + 1$, we provide an algebraic construction of an ideal whose projective dimension is equal to $i$ if and only if the characteristic divides $n$.
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