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Jul
29
awarded  Good Answer
Jul
29
comment Genus of a plane curve of the form $\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$
It depends on whether genus means arithmetic or geometric genus. Of course, you and probably the OP mean the latter.
Jul
28
awarded  Nice Answer
Jul
27
awarded  Nice Answer
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
Yes, I believe 2 and 3 are still open. Serre, in one of his books, asked explicitly whether the Higman group occurs as the fundamental group of a smooth projective variety. If so, it would provide a counterexample to 2. I'm not aware of any progress on this.
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
It's kind of a shame that the name "good group" seems to have stuck. Given the large community of mathematicians here, I wonder if can vote to change it to something more else. How about "Serre group"?
Jul
26
revised Relationship between étale and topological $K(\pi,1)$s
added 323 characters in body
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
The point of going to level $\ge 3$ is that $\Gamma(n)$ acts without fixed points, so you can use the usual $\pi_1$.
Jul
25
answered Relationship between étale and topological $K(\pi,1)$s
Jul
25
comment Relationship between étale and topological $K(\pi,1)$s
I strongly suspect that the main question is false, but I'll need to think more about it. There is a typo in 2 by the way. 2 and 3 are open as far as I know. Although there exists smooth projective varieties with non residually finite fundamental groups (Toledo,...).
Jul
24
revised Intuition behind the Kodaira Vanishing Theorem?
added 361 characters in body
Jul
23
revised Intuition behind the Kodaira Vanishing Theorem?
edited body
Jul
23
answered Intuition behind the Kodaira Vanishing Theorem?
Jul
21
awarded  Nice Answer
Jul
18
awarded  Nice Answer
Jul
11
awarded  Guru
Jul
8
awarded  Enlightened
Jul
7
awarded  Nice Answer
Jul
6
revised About Abhyankar's conjecture
added 6 characters in body
Jul
6
answered About Abhyankar's conjecture