9,231 reputation
12345
bio website cube.fredrikmeyer.net
location Oslo, Norway
age 25
visits member for 4 years
seen 13 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.


1d
awarded  Necromancer
2d
awarded  Constituent
Dec
17
answered Why do intersection of two quadratic forms implies elliptic curve?
Dec
17
comment Help understanding the proof of a theorem about Cohomology of Vector Bundles
You could try emailing the authors of the article, explaing that you have tried asking elsewhere.
Dec
13
comment Products of Varieties
Dear Georges, excellent answer as usual, but I'm interested in those pathologies (?) you mention at the end. What are examples of schemes with empty product (ah, maybe $Spec \mathbb Z/2 \times Spec \mathbb Z/3$?)? And what are examples of spaces with infinite product? (ah, maybe $Proj k[T] \times Proj k[T]$?).
Dec
10
comment An elementary Algebraic Geometry text, similar to Kempf's Algebraic Varieties
Have you looked into Eisenbud and Harris' "Geometry of Schemes"? It doesn't cover cohomology, but except from that, it is a very good book.
Dec
10
comment Is the cone over Grassmannian manifold $Gr_2(\mathbb{C}^n)$ an open set of a determinantal variety?
Ah, I hadn't thought of that! Thank you, that made the question a lot more interesting.
Dec
10
comment Is the cone over Grassmannian manifold $Gr_2(\mathbb{C}^n)$ an open set of a determinantal variety?
I don't think so. If you take the simplest nontrivial Grassmannian, namely $Gr(2,4)$, its equation in $\mathbb P^5$ is $x_0x_1-x_2x_4+x_3x_5$ - of degree $2$. But every determinant of degree $2$ is binomial.
Dec
9
comment Suppose that $a$ and $b$ belong to a commutative ring $R$. If $a$ is a unit of $R$ and $b^{2}=0$ . Show that $a+b$ is a unit of $R$
@downwoter: It would help if you also gave a reason for the downvote, so that I could improve my answers in the future.
Dec
9
answered Suppose that $a$ and $b$ belong to a commutative ring $R$. If $a$ is a unit of $R$ and $b^{2}=0$ . Show that $a+b$ is a unit of $R$
Dec
9
comment The intersection points are collinear
Terry Tao have a blog post about this and in particular answers your question, see here.
Dec
9
awarded  Caucus
Dec
8
comment Classifying complex conics up to isomorphism as quotient rings of $\mathbb{C}[x,y]$
An affine variety is connected if the coordinate ring is not a direct product of two nonzero rings. If we are two believe the first exercise in Hartshorne, then there are two isomorphism classes of irreducible conics in $\mathbb C^2$.
Dec
7
answered Calculating of genus of a curve
Dec
7
comment Calculating of genus of a curve
Then what genus are you talking about? If the curve is not smooth, the arithmetic genus and the geometric genus are different.
Dec
6
comment Calculating of genus of a curve
Indeed: as long as the curve $C$ is smooth, the genus only depends on the degree of the defining homogeneous polynomial.
Dec
3
answered Show that quotient rings are not isomorphic
Dec
3
answered Irreducible components of affine variety
Dec
2
comment Computing Resultant of Two Polynomials
@daOnlyBG Whups, yes that was a typo. But the method is clear?
Dec
2
answered Computing Resultant of Two Polynomials