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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

77 votes

Examples where it's useful to know that a mathematical object belongs to some family of objects

In a way, you can think of calculus as using exactly this sort of idea. Say you are interested in determining the area of the region consisting of points (x,y) with $a \le x \le b$ and $0 \le y \le …
3 votes
2 answers
910 views

Quartic Space Curves

It is an exercise in Hartshorne to classify nonsingular quartic curves in projective 3-space. I am interested in what happens when we allow singularities. In particular, I am looking for an explanatio …
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