The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. ...

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Projection of a curve in $\mathbb{P}^3$

I've been reading the proof of Theorem IV.3.10 in Hartshorne (p. 313 - 314), which states the following: Given a curve $X \subset \mathbb{P}^3$, there is a point $O \notin X$ such that the ...
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How to complete Vakil's proof that the composition of projective morphisms are projective when the target is quasicompact?

For this question, a morphism $\pi : X \rightarrow Y$ is projective iff there exists a finite type quasicoherent sheaf $\mathcal{E}$ on $Y$ such that $X$ is isomorphic (as a $Y-$scheme) to a closed ...