8,514 reputation
11943
bio website cube.fredrikmeyer.net
location Oslo, Norway
age 25
visits member for 3 years, 10 months
seen 7 hours ago

I'm a PhD Student at the University of Oslo, studying algebraic geometry. Emphasis on combinatorial aspects, like Stanley-Reisner rings and deformations.


8h
awarded  Explainer
1d
comment Zero divisors in $A[x_1,x_2,\dots,x_r]$
Here are some observations: You know from the $n=1$ case that if $f \in A[x_1,\cdots,x_n]$ is a zerodivisor, it is killed by an alement in $A[x_1,\cdots,x_{n-1}]$. Now $f$ is contained in a finitely-generated (free) $A[x_1,\cdots,x_{n-1}]$-module $M$ (take the generators to be the powers of $x_n$ in $f$). Then multiplication by $g$ defines an endomorphism $M \to M$, and $f$ lies in the kernel. In particular, multiplication by $g$ is a diagonal action. Maybe Cayley-Hamilton can be applied?
1d
comment Are smooth varieties locally isomorphic to the affine space?
What is true however, is that the completions of the local rings are all isomorphic to $k[[x_1,\cdots,x_n]]$, which is the same as for $\mathbb A^n$. Thus, smooth varieties are "analytically locally isomorphic to $\mathbb A^n$".
Sep
17
awarded  Popular Question
Sep
1
answered proving an algebraic set is irreducible
Aug
28
comment Thinking About Fractional Ideals Geometrically
Fractional ideals of $\mathbb Z$ correspond to line bundles (or invertible sheaves, or locally free sheaves of rank $1$) on $\mathrm{Spec} \mathbb Z$.
Aug
25
awarded  Notable Question
Aug
17
comment Geometrical description of maps of schemes
A map from $Spec \mathbb C[z]/z^2$ to $\mathbb A^2$ correspond to a tangent vector of the latter.
Aug
16
comment Looking for a smooth curve that is not rational
The intersection of two quadrics in $\mathbb P^3$ is an elliptic curve.
Aug
11
comment I need help to understand blowups of points in curves in $\mathbb A^2$
@user42912 That is correct. I recommend Chapter I, section 4 of Hartshorne's book. It is a very concise introduction to blowups in the end of the section, giving the equations.
Aug
10
revised Going Down Theorem, AM
added 90 characters in body
Aug
10
revised I need help to understand blowups of points in curves in $\mathbb A^2$
added 479 characters in body
Aug
10
answered I need help to understand blowups of points in curves in $\mathbb A^2$
Aug
6
awarded  Enlightened
Aug
6
awarded  Good Answer
Aug
6
awarded  Nice Answer
Aug
2
comment Extension of the field of scalars.
@HansGiebenrath Thank you for the comment. I've removed my flawed example.
Aug
2
revised Extension of the field of scalars.
added 7 characters in body
Jul
20
comment Why do only fixed points contribute to the Euler characteristic?
An algebraic scheme is usally defined as a scheme of finite type.
Jul
10
awarded  Good Question