Intereting Posts

Integration by Parts? – Variable Manipulation
Multiplication of a random variable with constant
The Riemann zeta function $\zeta(s)$ has no zeros for $\Re(s)>1$
How to show that $\int_0^\infty\frac{\ln x}{1+x^2}\mathrm dx=0$?
Matrices A+B=AB implies A commutes with B
Integrating $\int^{\infty}_0 e^{-x^2}\,dx$ using Feynman's parametrization trick
Quotient spaces $SO(3)/SO(2)$ and $SO(3)/O(2)$
Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?
Cartesian Product of Two Complete Metric Spaces is Complete
Eccentricity of an ellipse
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
Quotient group $\mathbb Z^n/\ \text{im}(A)$
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
When we say, “ZFC can found most of mathematics,” what do we really mean?
How to prove a set of positive semi definite matrices forms a convex set?

Suppose that $V\subset {\mathbb C}^n$ is an affine subvariety of codimension $p$. How does one prove that $V$ is regular (i.e., is a smooth manifold) at its generic points?

In view of the Jacobian test for regularity (which is just the implicit function theorem in this case), it suffices to show that there exist a point $x\in V$ and polynomials $f_1,…,f_p$ in the defining ideal $I$ of $V$ so that the derivatives $df_1,…, df_p$ are linearly independent at $x$. However, I do not see why such point and polynomials would exist.

- Polynomials vanishing on an infinite set
- Isomorphisms (and non-isomorphisms) of holomorphic degree $1$ line bundles on $\mathbb{CP}^1$ and elliptic curves
- When does a line bundle have a meromorphic section?
- For $(x+\sqrt{x^2+3})(y+\sqrt{y^2+3})=3$, compute $x+y$ .
- Hartshorne Theorem 8.17
- $\mathbb{A}^2\backslash\{(0,0)\}$ is not affine variety

- A question about Hartshorne III 12.2
- The uniqueness of a special maximal ideal factorization
- Original works of great mathematician Évariste Galois
- Normal at every localization implies normal
- Characterization of ideals in rings of fractions
- Does there exist such an invertible matrix?
- Local ring on generic fiber
- $R^n \cong R^m$ iff $n=m$
- Relation between n-tuple points on an algebaric curve and its pre-image in the normalizing Riemann surface
- Separated scheme

- Exercises about Hausdorff spaces
- inverse of diagonal plus sum of rank one matrices
- understanding the basic definition
- Why the need of Axiom of Countable Choice?
- Can a real symmetric matrix have complex eigenvectors?
- Associativity of Day convolution
- Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
- Are vectors and covectors the same thing?
- Lines in the plane and recurrence relation
- Monkey typing ABRACADABRA and gamblers
- “Proof” that $\mathbb{R}^J$ is not normal when $J$ is uncountable
- Is there finest topology which makes given vector space into a topological vector space?
- Induction without a base case
- The measurability of convex sets
- showing that the sequence $a_n=1+\frac{1}{2}+…+\frac{1}{n} – \log(n)$ converges