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seen Jun 5 '13 at 0:57

Math! :)


Apr
5
accepted A linear subspace of projective space
Apr
5
accepted Is primitivity invariant under matrix conjugation.
Apr
5
accepted Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
Apr
5
revised Harris' AG ex 2.24: projective variety under regular map.
added 17 characters in body
Apr
5
comment Harris' AG ex 2.24: projective variety under regular map.
I am not saying $\phi_i$ is a regular map, but $\phi=[\phi_0:\ldots:\phi_i:\ldots:\phi_k]$ is a regular map, right? I completely believe you that the machinery of schemes is useful here, but I don't think it's necessary given that it's given in chapter 2 of Harris book.
Apr
5
comment Harris' AG ex 2.24: projective variety under regular map.
How is that identity not of that form? Isn't the identity just that with $\phi_i([X_0:\ldots:X_k])=X_i$? If I were to assume all regular maps were of this form where each $\phi_i$ is homogenous, do you have any advice for the question? I agree with you that this form of a regular map does not cover all of them, as I've read in Harris's book.
Apr
5
asked Harris' AG ex 2.24: projective variety under regular map.
Apr
5
comment Given $\sum |a_n|^2$ converges and $a_n \neq -1$, show that $\prod (1+a_n)$ converges to a non-zero limit implies $\sum a_n$ converges.
It may very well be, my teacher just put it on the problem set. He took problems from lots of different books without citing them, sometimes because he made minor changes.
Apr
3
revised Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
deleted 4 characters in body
Apr
3
asked Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
Mar
31
awarded  Civic Duty
Mar
31
comment Problems with votes
please complete the question
Mar
31
accepted Polynomials vanishing and non-intersecting varieties.
Mar
31
asked Polynomials vanishing and non-intersecting varieties.
Mar
29
comment A linear subspace of projective space
Is it easy to show that the "biggest" linear proper linear subspace is a hyperplane? And thus, by what you've shown since it cannot be contained in that, it must be the whole thing?
Mar
29
comment A linear subspace of projective space
how do we know there cannot be more than one hyperplane? is the span of two distinct hyperplanes the whole space necessarily?
Mar
29
asked A linear subspace of projective space
Mar
25
accepted Do complex eigenvalues of a real matrix imply a rotation-dilation?
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
I see what you mean. My above method is correct too, right?
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
Are the two $\lambda$ different? Just say $v=cw$ where $c$ is real nonzero. Then we have that $av-bw=L(v)=L(cw)=c(bv+aw)$. Then what do I take the difference of? I am just saying $0=L(v-cw)=(av-bw)-c(bv+aw)=(a-bc)v-(b+ca)w=(a-bc)cw-(b+ca)w=(ac-bc^2)w-(b+ca)w=‌​(-b-bc^2 )w=0$. So $b=-bc^2$. If $b\neq0$ then $c^2=-1$, a contradiction to $c$ is real.