Abstract In this paper, we address the postulation problem of zero‐dimensional schemes of length at most 4 on a surface. We prove some general results and then we focus on the case of , and Hirzebruch surfaces. In particular, we prove that except for few well‐known exceptions, a general union of schemes of length at most 4 has always good postulation in and in .
Ballico et al. (Sun,) studied this question.