This post was translated from Korean by LLM (Kimi). The translation may contain errors or awkward sentences. The Korean original is the source of truth.
We now turn to closed subschemes of \(\mathbb{P}_\mathbb{K}^n\) as examples of closed subschemes. \(\mathbb{P}^n\) is somewhat more complicated than an affine scheme, but still more manageable than a general scheme, because by §Projective Schemes, ⁋Definition 4, any closed subset of \(\mathbb{P}^n\) can always be written as the zero set of homogeneous polynomials in \(\mathbb{K}[\x_0,\ldots, \x_n]\). That is, although these homogeneous polynomials are not functions defined on \(\mathbb{P}^n\), we can nevertheless use a method almost identical to that for affine schemes, at least when representing closed subsets.
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