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Mar
7
comment True or False: $f$ is injective if and only if $f^*$ is surjective where $f^*$ is corresponding to the pullback to $f$.
Of course, you can easily turn this into a direct proof, which is then more elegant. But it is late, and I will leave you with this.
Mar
7
answered True or False: $f$ is injective if and only if $f^*$ is surjective where $f^*$ is corresponding to the pullback to $f$.
Mar
6
comment Can a birational morphism surject from an affine to a projective variety?
@AlexYoucis: What is the argument for the fact that it has an inverse on some $U\subseteq Y$ whose complement is codim. 2? The approach sounds interesting!
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@karl_christ: No, I mean surjective. Every fiber is nonempty.
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@karl_christ: Such a map would only give me an isomorphism of a dense open subset $U\subseteq X$ with another dense open subset $V\subseteq Y$ of $Y$. This proves nothing.
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@KReiser: Yea, I edited my question, this only makes sense for irreducible varieties.
Mar
4
revised Can a birational morphism surject from an affine to a projective variety?
added 41 characters in body
Mar
4
awarded  Electorate
Mar
4
answered Isomorphism between End$(V)\otimes A$ and End$_A(V\otimes A)$.
Mar
3
comment Can a birational morphism surject from an affine to a projective variety?
@Ben: I am not so much interested in pathologic cases, you may safely assume that all the objects are actually interesting.
Mar
3
asked Can a birational morphism surject from an affine to a projective variety?
Mar
3
asked Resolution of singularities of the determinant hypersurface
Mar
1
answered Orbits of algebraic groups (dimension of connected components)
Feb
27
comment Is this graph theory problem NP-Complete?
What I ment to say is: I expect the answer to be a resounding "we still don't know", all we know that it is in P.
Feb
27
comment Is this graph theory problem NP-Complete?
Technical nag: Your problem is not a decision problem, so it would at best be NP-hard. However, you can do DFS from each vertex to find all cycles in which that vertex is contained. This sounds like polynomial time to me, and if you can prove that the problem is not NP-hard, then you would have shown P$\ne$NP.
Feb
27
comment Qing Liu's definition of an algebraic variety, a non-separated line
This is a big problem with the notion of "variety" that has bugged me for quite some time as well: There is no really good consensus about what the word precisely means.
Feb
19
answered Covers with fixed ramification
Feb
19
awarded  Nice Question
Feb
18
comment Covers with fixed ramification
From your notation I take it that $D$ is an effective (Weyl) divisor? In other words, a codimension one subvariety? Because the multiplicities of that divisor are quite meaningless for the ramification question at hand. Also. Is $D$ base point free by any chance?
Feb
16
answered Which rational functions $\mathbb{P}^1\rightarrow k$ are regular at the point at infinity?