query: If $F(r+p)$ is gen. by gl. sect. & $H^0(P^n,F(r))\otimes H^0(P^n,O_{P^n}(p))\rightarrow H^0(P^n,F(r+p))$ is surj, why is $F(r+p)$ gen. by gl. sect.?
positive_passages.docid: 145820
positive_passages.text: Mumford's regularity theorem
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 121479
negative_passages.text: Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 114267
negative_passages.text: If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?
negative_passages.docid: 122603
negative_passages.text: How does $\mathcal E(\rho)=\mathrm{Tr}_{env}[U(\rho\otimes\rho_{env})U^\dagger]$ turn into $P_0\rho P_0+P_1\rho P_1$?
negative_passages.docid: 146480
negative_passages.text: Example of $\deg(fg)<\deg(f)+\deg(g)$
negative_passages.docid: 7870
negative_passages.text: For $M\otimes_R N$, why is it so imperative that $M$ be a right $R$-module and $N$ a left $R$-module?
negative_passages.docid: 15387
negative_passages.text: Order of $GL(n, \mathbb Z_p)$
negative_passages.docid: 95976
negative_passages.text: Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 137669
negative_passages.text: $P$ is a monic polynomial of degree $n$ , then which are correct?
negative_passages.docid: 41363
negative_passages.text: when is f@g not the same as f[g]?
negative_passages.docid: 83542
negative_passages.text: A natural problem in $\textrm{S}_2^\textrm{P}$?
negative_passages.docid: 21954
negative_passages.text: A question about $f(x)\equiv 0$
negative_passages.docid: 142014
negative_passages.text: study of subspace generated by $f_k(x)=f(x+k)$ with f continuous, bounded..
negative_passages.docid: 45179
negative_passages.text: When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?