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Feb
11
awarded  Popular Question
Jan
21
accepted Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
Jan
13
comment Characterization of the $m$-torsion points of an elliptic curve.
Oh, nice. Now it makes sense to me...
Dec
31
comment Characterization of the $m$-torsion points of an elliptic curve.
Sorry, may I ask: what do you mean by $\omega^i$?
Dec
31
comment Algebraic methods to compute the cohomology ring of the complex topology of a variety?
But any projective curve will become affine once you delete one point...
Dec
30
comment Tate conjecture for Fermat varieties
I thought in the situation that X dominant Y, then you can express chow group of Y as a subspace of chow group of X, the same for etale cohomology. So then you will get that T(r) for X imply T(r) for Y. And we know that Fermat Varieties are dominated by product of Fermat curves, and Tate's conjecture holds for product of curves. Then we'd conclude that T holds for Fermat Varieties. But maybe I was wrong...
Dec
25
comment Tate conjecture for Fermat varieties
Also, I know very little about Tate's conjecture about cycles of arbitrary codimension. But isn't it true that if X dominant Y of same dimension and T(r) holds for X would imply T(r) holds for Y?
Dec
25
comment Tate conjecture for Fermat varieties
Have you looked at Shioda and Katsura's paper projecteuclid.org/download/pdf_1/euclid.tmj/1178229881 and Ulmer's paper arxiv.org/pdf/math/0109163.pdf ?
Nov
30
comment Inequality about the euler characteristic of surfaces
The singular fibre should have smaller Euler characteristic than generic fibre. If you are still confused maybe I can write an answer about it...
Nov
29
comment Calculation with Leray spectral sequence
Maybe you can try to see the Cohomology of an elliptic surface by Leray SS? Have you tried that?
Nov
29
comment Fundamental group of the complement homogeneous variety in $\mathbb{C}P^{2}$
At least both $H_1$'s vanish by Poincaré duality and some exact sequence.
Nov
29
answered About an example of normal bundle of a curve over a surface
Nov
29
comment algebraically closed fields of characteristic 0 and $\mathbb{C}$
@whacka $ Q\bar$ and algebraic closure of $ Q\bar (t)$ have same cardinality (both countable infinite), but they are definitely different... I think you meant cardinality of transcendental basis?
Nov
28
comment About an example of normal bundle of a curve over a surface
I only know $h^0(C,O_C(H))$ is between 6 to 8... As $h^0(P^6,H)=7$, and we know $2H=K$. I would guess the number is 8 generically, but I don't know how to prove it.
Nov
28
comment local ring of a smooth point
Ok, then according to your definition. Regular means $dim_km/m^2=dim A$, so local ring is regular iff 'your definition of smooth point'. However, as Mohan pointed out, the more often seen definition of smoothness is somehow a relative version. With a scheme along we can only talk regularity but not smoothness.
Nov
28
comment local ring of a smooth point
What's your definition of smooth point? Do you assume your ring to be a k-algebra?
Nov
27
asked Asking for some exercises to help me understanding abelian varieties better?
Nov
18
awarded  Yearling
Nov
10
awarded  Popular Question
Nov
3
comment hairy ball thm. and projective space
I'm not an expert in topology, but if my memory was right, they ARE orientable...