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visits member for 4 years, 9 months
seen Jul 17 at 21:45

Jul
2
awarded  Curious
Mar
11
comment Automorphisms of a smooth quadric surface $Q\subset\mathbb{P}^{3}$
Any automorphism must preserve the intersection product, so it either preserves or exchanges the two rulings. Using this you should be able to prove what you want.
Mar
11
awarded  Citizen Patrol
Feb
27
awarded  Nice Question
Feb
5
comment Who stated and proved the “Hopf lemma” on bilinear maps?
@QiaochuYuan: added clarification in the body of the question.
Feb
5
revised Who stated and proved the “Hopf lemma” on bilinear maps?
clarification in reply to a comment
Feb
4
comment Who stated and proved the “Hopf lemma” on bilinear maps?
This is really relevant, and seems to support the idea that, after Hopf's work, the result became known (even for an arbitrary algebraically closed field, not C!) But Saint-Donat does not even mention Hopf or anybody else...
Feb
4
asked Who stated and proved the “Hopf lemma” on bilinear maps?
Feb
4
comment Symmetric product of global sections on a curve
@aginensky I see, thanks.
Feb
3
comment Symmetric product of global sections on a curve
Is it easy to see that $\dim W\ge 2\dim V-1$? Is it in Arbarello-Cornalba-Griffiths-Harris? Or on some other reference? Thanks.
Feb
3
comment Why aren't fields called “bodies” instead?
In European Spanish it is "cuerpo" indeed, but it is "campo" in Mexican Spanish, clearly by US influence. I don't know how far south in America this goes, nor whether they use "cuerpo" for skew fields. By the way, I believe that in Spain skew fields are generally called "anillos de división" (division rings) but "cuerpos no conmutativos" is not unheard of.
Dec
22
comment Is Euclid dead?
Then my point was, bullshit like this can come in even with proofs in the curriculum.
Dec
22
comment Is Euclid dead?
Also, it seems perfectly possible that critical thought existed, but that for a sufficiently large mass of young people the bullshit had stronger impact than the proofs. I simply don't know.
Dec
22
comment Is Euclid dead?
@SergeiAkbarov, quid and quim are different people! ;) I don't really know the soviet system to argue with you at all aobut it, but it seemed to me that your position was, "if you take proofs out of the curriculum, bullshit like this will come in instead." Maybe it was Petrunin's comment which I attributed to you.
Dec
22
comment Is Euclid dead?
@SergeiAkbarov, I think Latin fell out of the western curricula more or less at the same time as Euclidean Geometry. Some little Philosophy and Logic do remain (at least in some countries). Anyway, how much faith can one retain that teaching proofs, in itself, will be determinant for building critical thought? Isn't the USSR system that you explain a counterexample?
Nov
20
comment Deformation of a family of curves in a surface
Do you mean, for each divisor in U there is a deformation of S which contains it?
Nov
20
comment Deformation of a family of curves in a surface
Probably it would help to get answers if you give some motivation for the question (what are you after? which kind of conditions would be ok in your setting?) Something that confuses me: are you assuming Hilb_{P,Q} irreducible? If so, what does this imply on the pair, (P,Q)? Otherwise, what does "a general element" mean?
Nov
19
awarded  Yearling
Oct
12
comment Nagata's conjecture in positive characteristic
Now that I think of it, toric degenerations as those used by Ciliberto-Miranda and (implicitly) Yang, Dumnicki, Eckl, ... should work in char=p as well. Only when Ciliberto-Miranda need a tansversality lemma (for matching conditions) char=0 is probably necessary (one should check). So (grosso modo) their results on Seshadri constants are ok in arbitrary characteristic, but some results on SHGH are only char=0, and also our results on "good rays" (passing from the large inequality in Nagata-like bounds to the strict one).
Oct
12
comment Nagata's conjecture in positive characteristic
By the way, I am greatly interested in estimations obtained via tropical geometry, even if they were currently not the best.