# What is the function field of a hyperplane?

If $X\subset\mathbb{P}^n$ is a hyperplane, what is the function field $K(X)$ ? Is $K(X)$ just k?

-

6
A hyperplane is isomorphic to $\mathbb{P}^{n-1}$. Do you know what the function field of $\mathbb{P}^{n-1}$ is? – Qiaochu Yuan Nov 29 '12 at 0:55
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8639553785324097, "perplexity_flag": "head"}