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Oct
8
answered Constructing realizations of Hilberts weak Nullstellensatz?
Oct
5
comment Algebra of invariants finitely generated
Definitely true if $k$ is of characteristic zero. A reference would be 27.4 in the book Lie algebras and algebraic groups by Tauvel & Yu.
Oct
5
comment Prove of Sheafication of sheaf is a sheaf isomorphism
In other words, what is your definition of sheafification? Also, to be on the safe side, how do you define presheaf and sheaf? =)
Sep
24
comment Euler character of etale finite cover
@poorna: sounds like a tame situation, but I don't know. Euler characteristic is sensitive to removing a finite set of points, so I am unsure. I think it might be best to ask this as a separate question, I am sure someone will know better.
Sep
23
comment Euler character of etale finite cover
@poorna: Ok, I was a bit slow there. But assuming that $\pi$ is etale outside a finite set of points does not even guarantee that the morphism is finite, it could for instance be the blow-up of a singular surface. I suspect one might be able to construct counterexamples this way.
Sep
23
comment Euler character of etale finite cover
@poorna: We need Hirzebruch-Riemann Roch only for the Bundle $\mathcal O_{\tilde X}$ on the smooth variety $\tilde X$, which works. The Lemma requires the morphism $\pi:\tilde X\to X$ to be flat and finite, according to Fulton. I would assume that this condition can not be left out. Flatness is implicit if both $X$ and $\tilde X$ are regular. So, I think it works if you can show that $\pi$ is flat. I do not know off the top of my hat if your conditions imply that, though. Flatness is quite hard to grasp for me. If something comes to mind, I will post it.
Sep
23
revised Euler character of etale finite cover
added 18 characters in body
Aug
30
awarded  Self-Learner
Aug
12
revised Why would we a priori expect $V(I)$ to satisfy axioms to define the closed sets for a topology on $\text{Proj}(S)$?
added 873 characters in body
Aug
5
comment Continuous maps are morphisms of varieties?
Why are $g\circ\phi$ and $h\circ\phi$ polynomials?
Aug
4
revised $A+B+C=2149$, Find $A$
deleted 51 characters in body
Aug
4
answered $A+B+C=2149$, Find $A$
Aug
4
comment Why would we a priori expect $V(I)$ to satisfy axioms to define the closed sets for a topology on $\text{Proj}(S)$?
Whoops, if you liked the reply then here it is again. I thought I might have misunderstood your question =).
Aug
4
answered Why would we a priori expect $V(I)$ to satisfy axioms to define the closed sets for a topology on $\text{Proj}(S)$?
Jul
28
comment Finding a path in a graph by its hash value
At this point you'd need to make the question more formal, I think. What are your exact requirements and what properties does the hash function have?
Jul
28
answered Finding a path in a graph by its hash value
Jul
27
comment Finding a path in a graph by its hash value
This is trivially possible if there are finitely many vertices, so I assume there is an infinite number of vertices - but in this case, there could be infinitely many paths of length $n$, how are you "given" all these hash values?
Jul
17
comment Algorithmic question about algebraic varieties and affinely independence
What precisely is your input and what is your algorithm allowed to do? If you are allowed to use randomization for example, just pick the $u^{(i)}$ randomly and you'll be fine.
Jul
16
answered Reference request for a theorem on maps to normal varieties with equidimensional fibers being open
Jul
13
comment Fiber dimension theorem for locally closed sets
@guest_09072015: Yes, this is true, but simply because a nonempty, open subset of an irreducible algebraic variety is again an irreducible algebraic variety. It might not be affine, but it is a variety.