Reputation
89,326
Next tag badge:
379/400 score
86/80 answers
Badges
4 111 219
Newest
 Good Answer
Impact
~645k people reached

10h
comment The set of polynomials which “cut out” smooth subsets of projective space is open and dense
How can it be shown in characteristic $p$ that for each $d$ there is a smooth hypersurface of degree $d$ in $ \mathbb P^n$ ?
1d
awarded  Good Answer
Feb
6
revised Closed points in projective space correspond to which homogenous prime ideals in $k[x_0,…,x_n]$
added 324 characters in body
Feb
6
answered Closed points in projective space correspond to which homogenous prime ideals in $k[x_0,…,x_n]$
Feb
6
comment Affine varieties and their ideals
Dear Sfarla, don't worry: everybody has such moments, Grothendieck included !
Feb
6
revised Affine varieties and their ideals
added 9 characters in body
Feb
6
comment Affine varieties and their ideals
Dear jacob, I have taken the liberty to change your $I(V):I(W) = I(V/W)$ (in the third line) into the correct $I(V):I(W) = I(V \setminus W)$
Feb
6
comment Affine varieties and their ideals
Your part 2. seems to be false. Indeed, in your very last line $Z(I)\setminus Z(J)$ is the set of points $(\alpha,1)$ with $(1,1)$ deleted, whereas $Z(I:J)$ is the set of all $(\alpha,1)$, including $(1,1)$ .
Feb
5
revised Affine varieties and their ideals
added 232 characters in body
Feb
5
answered Affine varieties and their ideals
Feb
5
reviewed Approve Line bundles of the circle
Feb
3
comment proof that an arbitrary homeomorphism $h: B_{1}[0] \rightarrow B_{1}[0]$ maps $S^n$ to $S^n$
Dear @Arthur: I'd love to read a proof of your assertion...
Feb
1
comment Rank of Jacobian Matrix for the Stereographic Projection
The set $S^n$ is a submanifold of $\mathbb R^{n+1}$: this is completely trivial because it is the zero locus of$ f(x)=\sum x_i^2-1$ and $grad(f)(x)\neq0$ for $x\in S^n$. The notion of submanifold of $\mathbb R^k$ is just advanced calculus and is independent of the much more advanced rigmarole about atlasses and their compatible charts :-) Of course if you insist on proving that your matrix has maximal rank go ahead, but that will be a dreary algebra exercise with zero geometrical content. However I agree that it is always more prudent to do what your professor wants...
Feb
1
answered Rank of Jacobian Matrix for the Stereographic Projection
Jan
31
comment Motivation for studying rational curves
Shafarevich, Basic Algebraic Geometry, Volume 1 pages 4,5,9,171,174. By the way, every page of that book is worth reading!
Jan
31
comment Motivation for studying rational curves
Thanks, @Remy: I have changed my gallicism rectangular triangle to right angled triangle in my answer. Although almost everything I read in the professional mathematical literature is in English, I don't know the English terminology of elementary mathematics so well, since as a child everything I read or heard was of course in French. For example I only recently learned the complicated word protractor :-)
Jan
31
revised Motivation for studying rational curves
added 242 characters in body
Jan
30
revised Motivation for studying rational curves
added 410 characters in body
Jan
30
comment Motivation for studying rational curves
Dear kk lm, don't worry: rational curves are beginners stuff, despite the efforts of some books and people to hide that fact :-) I'll show that below.
Jan
30
answered Motivation for studying rational curves