1,704 reputation
417
bio website mathoverflow.net/users/15289/…
location Princeton, NJ
age 24
visits member for 2 years, 6 months
seen 2 days ago

My nickname is jerrysciencemath which is also my display name before.

I am now a second year grad student at Princeton.

I am interested in algebraic geometry, differential geometry and topology.


Jul
2
awarded  Curious
Apr
18
awarded  Yearling
Mar
7
answered Does $\,f_* \mathcal{O}_{X_T} \cong \mathcal{O}_{T}$ hold in this situation?
Jan
13
awarded  Nice Answer
Nov
19
answered Why is it better to have the induced map by a line bundle $L$ into projective space map into $\mathbb P |L|^*$?
Nov
9
answered Poles of abelian differentials
Oct
25
comment Is the complement of a codimension 2 subvariety of an affine variety affine
Thanks for your answer!
Oct
25
answered Is the complement of a codimension 2 subvariety of an affine variety affine
Oct
23
comment Is a scheme with a single closed point affine?
I think you should require $X$ to be connected, otherwise the disjoint union of a scheme without closed points and the spectrum of a local ring is a counterexample.
Oct
21
comment Embedding $\mathbb A^2-(0,0)$ into $k^n$, the image is not closed
@AsalBeagDubh: Sure, thanks.
Oct
21
answered Embedding $\mathbb A^2-(0,0)$ into $k^n$, the image is not closed
Oct
14
comment Dimension of a meromorphic differentials space
Do these degree $k$ meromorphic differential forms have only simple poles at $z_i$?
Oct
13
revised Let $X=\operatorname{Spec} k[w,x,y,z]/(wz−xy)$. Show the Weil divisor cut out by $w=x=0$ is not locally principal.
added 122 characters in body
Oct
13
comment Let $X=\operatorname{Spec} k[w,x,y,z]/(wz−xy)$. Show the Weil divisor cut out by $w=x=0$ is not locally principal.
Dear @Gazerun, I have edited my answer by adding a proof of the affiness of $X-Z$.
Oct
13
revised Let $X=\operatorname{Spec} k[w,x,y,z]/(wz−xy)$. Show the Weil divisor cut out by $w=x=0$ is not locally principal.
add a proof of the affiness of $X-Z$
Oct
12
answered Let $X=\operatorname{Spec} k[w,x,y,z]/(wz−xy)$. Show the Weil divisor cut out by $w=x=0$ is not locally principal.
Sep
17
comment A Question on the bijection between ideal sheaf and closed subscheme
What does $\mathcal{O}_X/\mathcal{I}=\mathcal{O}_X/\mathcal{J}$ mean in the context? I think it is not saying that they are isomorphic (different closed embeddings from a same scheme can have same set-theoretic image), but they are isomorphic via the quotient of the identity map of $\mathcal{O}_X$, so of course $\mathcal{I}=\mathcal{J}$.
Sep
13
comment Computing germs of a projective curve
So that is why completion is necessary to study singularities?
Sep
9
comment The Disk and the Punctured Disk
Do you mean $\mathbb{C}[[t]]$ by the ring of formal power series? This ring is a discrete valuation ring, so $D$ contains only two elements $(0)$ and $(t)$, why do you say $D$ is a disk?
Sep
6
comment On verifying Proj S is a scheme
Why do you think $D_+(f)$ is homeomorphic to $Spec(S_f)$?