Timeline for Which object related to families of algebraic varieties over a scheme $ S $ corresponds to the tensor product of vector bundles?

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May 14, 2018 at 16:24	comment	added	Eric Canton		Suppose $L = \pi^*(\mathcal{O}(1))$ for some $\pi: X \to \mathbb{P}^n$. Then $L^{\otimes d}$ corresponds to the restriction of $\mathcal{O}(d)$, of course, but it is more geometric, perhaps, to think of this as the restriction of $\mathcal{O}(1)$ from the projective space that is the codomain of the $d$-uple embedding $\pi: X \to \mathbb{P}^n \to \mathbb{P}^N$. To generalize to vector bundles, you could consider maps into Grassmannians as well, for which there are $d$-uple embeddings (I know Harris goes through this in the same book you cite in your other post).
May 12, 2018 at 15:31	history	asked	YoYo	CC BY-SA 4.0