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Some useful questions and answers in MSE:
Number of $p$-subgroups (generalization of Sylow's theorem)
Correspondence between divisors and line bundles
What is a blow-up?
Localization does not commute with infinite products
Hilbert scheme of points in $\mathbb{A}$^2
Why does the tautological bundle $\mathcal{O}(-1)$ have no global sections?
If $E/F$ is algebraic, and each $f\in F[x]$ has a root in $E$, then $E$ is algebraically closed
Explicit formula for the discriminant of a quintic
Great answer about projectively normal varieties
a question about Del Pezzo surfaces
Normal bundle of complete intersection
Smooth rational curve of degree 4 contained in a unique quadric
Isomorphic v.s. projectively equivalent elliptic curves
TO DO:
http://math.stackexchange.com/questions/541545/exercise-ii-2-8-on-hartshornes-algebraic-geometry
https://math.stackexchange.com/questions/4330979/prove-graph-theory-by-probability
https://math.stackexchange.com/questions/2868779/a-bound-on-the-number-of-unit-perimeter-triangles
https://math.stackexchange.com/questions/3479403/szemer%c3%a9di-trotter-theorem-unit-area-triangles
https://math.stackexchange.com/questions/4592942/line-segments-in-the-plane-where-each-triple-can-be-intersected-by-a-common-line