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Nov
6
asked Again: Ample and very ample line bundles
Nov
5
comment Is a finite normal subgroup of a reductive algebraic group central?
@MarcvanLeeuwen: I think you misunderstood. I ment: Can you give an example of an infinite algebraic group $G$ which is not connected and such that a finite, normal subgroup $N\subseteq G$ exists which is not central? Because yes, I understand that a finite group $G$ is a counterexample, but I would like to know if there is an infinite counterexample.
Nov
5
comment Is a finite normal subgroup of a reductive algebraic group central?
@MarcvanLeeuwen: Can you give an example when we assume $G$ to be infinite, but not connected?
Nov
4
comment Is a finite normal subgroup of a reductive algebraic group central?
I will call $G$ reductive if its unipotent radical is trivial. Equivalently, you can use the definition that every finite-dimensional $G$-module is semisimple, i.e. a direct sum of irreducible $G$-modules.
Nov
4
asked Is a finite normal subgroup of a reductive algebraic group central?
Nov
1
comment The cone over a projective variety
@user42912: That's not quite correct, because $I(\mathbf 0)=(x_0,\ldots,x_n)$ is a homogeneous ideal, but of course it contains polynomials that are not homogeneous. You simply have $I(\pi^{-1}(Y))=I(\pi^{-1}(Y)\cup\{ \mathbf 0 \})=I(Y)$.
Oct
31
answered The cone over a projective variety
Oct
29
comment Simple example of an ample line bundle that is not very ample
Very helpful indeed, thanks for giving all these examples.
Oct
29
accepted Simple example of an ample line bundle that is not very ample
Oct
29
comment Simple example of an ample line bundle that is not very ample
Fascinating. This is presenting to be exactly the learning experience I had hoped it would be. I think I will have a close look at all of those ;).
Oct
29
comment Simple example of an ample line bundle that is not very ample
Hum, now I am confused. You wrote "Sections of K define a 2:1 cover, so K is globally generated but not ample." I think you simply mistyped then, because if that means it's a finite cover of degree $2$, then it is ample but not very ample. And that'd be what I want. In (2), you say it isn't globally generated and I thought that being globally generated is necessary for being ample.
Oct
29
comment Simple example of an ample line bundle that is not very ample
Unfortunately, it seems like only (3) really meets my requirements, because in the other cases the bundle isn't ample. I will have a look later.
Oct
29
awarded  Enthusiast
Oct
28
asked Simple example of an ample line bundle that is not very ample
Oct
23
answered How to prove that the following morphism is surjective?
Oct
21
answered Proof of Zariski Topology theorem
Oct
18
accepted Determinant vanishing over polynomial ring
Oct
18
answered Determinant vanishing over polynomial ring
Oct
18
revised transversal intersection Hartshorne Lemma V.1.2 p.358
added 17 characters in body
Oct
18
comment transversal intersection Hartshorne Lemma V.1.2 p.358
Errr. yes of course. Let me fix that.