Syzygies of $Gr_{2}(\mathbb{C}^4)$

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I'm going to start the study the problem of syzygies. I read on web that it is possible to compute syzygies of an algebraic variety for example $Gr_2(\mathbb{C}^4)$, but I don't understand how can I find syzygies of a variety because in my definition I can only calculate syzygies of a $R$-module $M$. Can you explain how can I find syzygies of $Gr_2(\mathbb{C}^4)$ and give me some reference?