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Born to be proud
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8 votes

The unit tangent bundle for submanifold $M^{m}\subset \mathbb{R}^{n}$ is a (2m-1)-dim submanifold

7 votes
Accepted

graded ring and homogeneous ideal

4 votes

$y^2 - x^3$ not an embedded submanifold

2 votes

Is there an example that $\mathcal{O}(\mathrm{Proj}\,B)\neq B_0$ for some graded ring $B$?

1 vote

Are these conditions equivalent to the definition of regular coordinate ball?

1 vote

How to show the existence of $\alpha_1,\cdots,\alpha_n$ as a basis of $L|K$ which is contained in $B$?

1 vote

Is the domain of the maximal integral curve of $N|_{\operatorname{Int}M} $ starting at $f_p(a)$ an open interval of the form $(-a,b)$?

0 votes
Accepted

How to show $UM$ is an embedded $(2m-1)$-dimensional submanifold of $T\Bbb R^n\approx \Bbb R^n\times \Bbb R^n$?

0 votes

How to show $d>0$?

0 votes

How to show $\coprod^n_{i=1}X_i\to S$ induced by $f_i$ is projective?

0 votes

How to show $\coprod^n_{i=1}X_i\to S$ induced by $f_i$ is projective?

0 votes

How to show the image of $U$ in $X'$ is dense?

0 votes

Can $dF_p:T_pM\to T_{F(p)}N$ be surjective?

0 votes

Do we have $a\otimes 1=0$ if and only if $a=0$?

0 votes

Is the canonical morphism of sheaves $f^{-1}f_*\mathcal F\to \mathcal F$ an isomorphism?

0 votes

Is the presheaf defined by $U\to \operatorname{Im}(\alpha (U))$ indeed a sheaf?

0 votes

Is the order of $ab^{-1}$ larger than $m$?

0 votes

Is $D(f)$ the smallest open set of $\operatorname{Spec}B$ such that $D_+(f)\subset D(f)$?

0 votes

How to prove the sufficient and necessary conditions of pullback square?

0 votes

How to show the set $\operatorname{Hom}_K(L,\bar{K})$ of all $K$-embeddings of $L$ is partitioned into $m$ equivalence classes of $d$ elements each?

-2 votes

Do we have $(gf)^*\mathcal F=f^*(g^*\mathcal F)$?