Let $I=(x_{1}^{2}-x_{2}x_{3},x_{3}^{2}x_{4},x_{1}x_{2}x_{3},x_{4}^{3})\subset S=K[x_{1},x_{2},x_{3},x_{4}]$ be an ideal. I am trying to compute its minimal graded free resolution.
Since $I$ has four generators three of degree $3$ and one of degree $2$ so $F_{0}=S(-2)\oplus S^{3}(-3)$. That is
$\cdots\rightarrow S(-2)\oplus S^{3}(-3)\rightarrow I\rightarrow 0$.
Next we need to find the kernel of $S(-2)\oplus S^{3}(-3)\rightarrow I$. Please help to find the kernel and complete the resolution.
2026-03-26 09:42:14.1774518134
Finding kernel of a map in a minimal free resolution of a graded ideal
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