Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
@JasonStarr i agree, but that was for weights equal to 1. And when all weights are equal, the second question has that answer an easy answer. In general, I was just looking whether there are conditions on sections of tensor powers of a line bundle to give a closed embedding.
Any morphism from a variety $ X $ to $ Hilb $ can be understood by understanding it on its geometric points. This is in Hartshorne (his original book) as the t-functor in chapter 2.
@user145752 the normal bundle of a line in P^n is n-1 copies of O(1). Now $ i^* \mathbb{P}^n $ sits in between O(2) and the normal bundle, so has to be the direct sum because of vanishing Ext..