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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 $\text{Proj}(S)$?
Aug
2
comment Generalization of Singular locus and non-free locus to an algebra
Shouldn't a definition be motivated by something? An example, if not a variety (no pun intended) of such, or some other observation? A lot of things can be defined, and one can probably make a lot of "similar" definitions, but they have meaning only if they formalize some concept that also warrants to have its own name.
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.
Jul
12
comment Fiber dimension theorem for locally closed sets
It is open in $\mathbb C^n$, but it can be given the structure of an affine variety. Inside $\mathbb C^{n}\times\mathbb C$, it correponds to the points $(z,t)$ subject to the polynomial condition $f(z)\cdot t = 1$.
Jul
9
answered Fiber dimension theorem for locally closed sets
Jul
5
revised Projection is an open map
cosmetics
Jul
5
comment Projection is an open map
@GFR: True & done. Thanks for the comment btw, I realize now that tomasz already pointed it out before but I completely overlooked that in his comment.
Jul
5
revised Projection is an open map
deleted 6 characters in body
Jul
5
comment Projection is an open map
@GFR: Indeed, that was a serious blunder. Should be fixed now.