Global regular function
= Global regular function
{title2=$f\in\Gamma(X,\mathcal O_X)$}
A global regular function is a <global section> of the <structure sheaf> of a <scheme>, defined on the entire scheme. These functions form its ring $H^0(X,\mathcal O_X)$. On an <affine scheme> this recovers the defining ring; on a positive-dimensional <projective complete intersection> it consists only of constants over the base <field>.