The only global section of the tautological line bundle on $\mathbb{P}^n$ is the zero section.
115142
Holomorphic functions on a complex compact manifold are only constants
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
39933
No holomorphic logarithmn
125212
How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
121995
Hilbert's Nullstellensatz implies $I(Z(I)) = \sqrt{I}$
93669
Is every embedded submanifold globally a level set?
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
112727
Surfaces in $\mathbb P^3$ not containing any line
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
26805
Non-Noetherian 0-dimensional ring
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
40502
The Degree of Zero Polynomial.
40996
Proving that free modules are flat (without appealing projective modules)
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
105014
Is the zero vector in $\mathbb{R}^n$ by itself a subspace of $\mathbb{R}^n$?
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?