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Apr
10
comment Schubert calculus: lines that intersect 4 given curves
You can think of cohomology as Chow ring and you can consider the map $q_*$ as push forward of cycle. For details, you can read section 1.4 of Fulton's intersection theory.
Apr
10
revised Locally finitely generated sheaf
added 374 characters in body
Apr
10
answered Locally finitely generated sheaf
Apr
10
answered Multiplication of three primitive roots
Apr
10
comment Prove that $|k(x)|\le C|x|^{-n}$ under suitable hypothesis on $k\in\mathcal{C}^1(\Bbb R^n\setminus\{0\})$
I am not very sure but I guess I have seen it in Stein's singular integral before.
Apr
10
comment What are the smooth map and the vector field in the Fig. 8.2, page 182 of John Lee's Smooth manifolds, 2nd
@TiWen The notion of pushforward of vector field is well defined if the smooth map is injective. Let X be the vector field on M. We can define the push forward f_*X pointwisely and it makes sense because there are no two points mapped to the same point.
Apr
10
comment Is function to unit vector is continuous?
The norm function is cts and never zero so 1/norm is continuous and mutiplication of functions are continuous...
Apr
10
answered What are the smooth map and the vector field in the Fig. 8.2, page 182 of John Lee's Smooth manifolds, 2nd
Apr
10
answered If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
Apr
10
comment If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
@DougM I think it is true if $f$ is decreasing but it is not true in general
Apr
7
comment Is $(1,0,…,0,-n^2,0,0,…) \in \ell^2$?
yes it is. for each $n$, no matter where $-n^2$ lives , the sum of squares of all entries is finite.
Apr
7
answered Dual representations of fundamental representations of a Lie algebra.
Apr
7
comment Understanding Weyl character formula and highest weight integrable representations
Given any abelian (semi)group $A$ , one can formally define $e(a)$ where $a\in A$ with property $e(a+b)=e(a)e(b)$. We usually write the (semi)group generated by $e(a),a\in A$ as $\mathbb{Z}[A]$
Apr
7
comment Do we have $\mathbb{C}[V^*] \cong S(V)$ or $\mathbb{C}[V] \cong S(V)$?
Right. That's a better explanation.
Apr
7
answered Do we have $\mathbb{C}[V^*] \cong S(V)$ or $\mathbb{C}[V] \cong S(V)$?
Apr
7
comment Relations of $S^2 V$ and heighest weight representations of Lie algebras.
The formula of dim of irreducible representation of highest weight $\sum_i a_i\omega_i$ is given by (15.17) of Harris and Fulton's representation theory (P.224)
Apr
7
answered Relations of $S^2 V$ and heighest weight representations of Lie algebras.
Apr
5
comment Assume that $I/J$ is a prime ideal of $R/J$, is $I$ a prime ideal of $R$?
do you assume $J\subset I$?
Apr
5
comment Projective curve $x^3+y^3=2z^3$ in $\mathbb P^2$ singular?
Using @Arthur's idea, all you need to do is to check when the Jacobian of $x^3+y^3-2$ is of rank $0$ and that's the place where the curve is singular and similar for the other two affine curves in A^2
Apr
5
comment For $f : V \to V$ a nilpotent endomorphism, with minimal polynomial $x^m$. Why $f^{m-1}(V) \subset ker(f)$?
nilpotent matrices have only zero as their eigenvalue so by Jardan canonical form, you are done