Some useful questions and answers in MSE:
Number of $p$-subgroups (generalization of Sylow's theorem)
Correspondence between divisors and line bundles
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:
Exercise II 2.8 on Hartshorne's Algebraic Geometry
Prove Graph theory by Probability
A Bound on the Number of Unit Perimeter Triangles
Szemerédi-Trotter theorem unit area triangles
Line segments in the plane where each triple can be intersected by a common line
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