/sci/ - Science & Math

>>10111668
I didn't know Spivak had a book on calculus, I must have thought it was 'calculus on manifolds'.
So you can't solve american calculus problems.

>>9647963
I can't read your latex, but isn't it just by definition? Studying moduli space of complex tori?

>>9648033
What's wrong about the generalization?

>>9647994
It is not an uncommon pain. Sometimes it has to be treated, see a doctor if it is still going on; recently it happened to a friend of mine, he had to take a little surgery and not fap for 1 month, he said it was hell. But at least you are not going to die. Sorry anon.
I still don't know what have you done so far, here are some exercises:

1) Let Y = V(x^2 - yz, xz-x) \subseteq A^3, show that Y is union of three irreducible closed sets (recall noetherianity), describe them and find their prime ideals;

2) assume char \neq 2, Y = V(x^2 + y^2 + z^2, x^2 - y^2 - z^2 + 1), decompose X into irreducible components;

3) Let Y = {(t,t^2,t^3) . t \in K} be the twisted cubic, show that Y is irreducible, has dimension 1 (find K[Y] and compute degree of trascendence of its quotient field, which equals krull dimension of Y) and describe its ideal I(Y);

4) consider the projective closure of twisted cubic, prove that its ideal is (x_0 x_2 - x_1^2, x_1 x_3 - x_2^2, x_0 x_3 - x_1 x_2).

If it is first time doing them they will be hard, the last more than the previous ones. Let me know if you want easier ones, equal ones, harder ones (we can move to surfaces and other stuff), hints or solutions. I'm also new to algebraic geometry, happy to know you.