13,150 reputation
11426
bio website
location
age
visits member for 4 years, 8 months
seen 2 hours ago

2h
comment Determinant of the oriented adjacency matrix of a tree
Expanding darij grinberg's comment --- it looks like the answer is $(-1)^n$ where $n$ is the number of "$v$-antioriented edges", i.e. the number of edges orientation of which should be switched to make all edges oriented from $v$.
2d
awarded  Enlightened
Nov
20
awarded  Nice Answer
Nov
19
answered Push-forward of locally free sheaves
Nov
11
awarded  Pundit
Nov
10
comment Analogue of Borel--Bott--Weil for General Equivariant Vector Bundles
It follows easily from the equivalence of the category of equivariant bundles and the category of representations of Borel subgroup, since Borel is solvable.
Nov
10
comment Analogue of Borel--Bott--Weil for General Equivariant Vector Bundles
On flag variety any equivariant vector bundle is an iterated extension of line bundles. So, its Euler characteristic can be computed by applying BBW to the factors and summing up.
Nov
7
answered When does a cubic surface pass through five lines?
Nov
6
comment Vector bundles on projective varieties
But, you can always embed a vector bundle into a TWIST of a trivial bundle.
Nov
4
comment What are the higher homotopy groups of a K3 suface?
I guess you could say that $V_3$ should be the kernel of the multiplication map $S^2H^2(X,Q) \to H^4(X,Q)$, so its dimension is $b_2(b_2+1)/2 - 1 = 252$. Of course this is equivalent to your computation, but does not require choosing a basis and a bit simpler.
Nov
3
comment What are the higher homotopy groups of a K3 suface?
But the higher homotopy gorups of an elliptic curve is easy to find, and this is definitely a better analogy for a K3 surface.
Oct
28
awarded  Enlightened
Oct
21
comment Why is it so hard to compute $\pi_n(S^n)$?
Probably, to check nontriviality of the Hopf bundle one can compute its Euler class?
Oct
14
comment The linear projection of projective spaces
@abx: of course the sign was wrong, now it is corrected, thanks!
Oct
14
revised The linear projection of projective spaces
added 2 characters in body
Oct
14
answered The linear projection of projective spaces
Oct
9
comment When is the Hodge diamond concentrated in $H^{n,n}$'s?
Cellular varieties have this property. But not only these. As for constructing a "related variety $X'$", I think there is no chance. What would you expect to get for a curve of positive genus?
Oct
5
comment G-equivariant coherent sheaves on Bott-Samelson Resolutions
Is the singularity of $X_w$ rational? If it is, then $Rf_*O = O$.
Oct
5
answered Intermediate Jacobians of intersections of two quadrics
Oct
4
comment Intermediate Jacobians of intersections of two quadrics
How do you define intermediate Jacobian over an arbitrary field? As for a twist, I can say that at the level of derived category the new feature is a sheaf of Azumaya algebras appearing on the curve. So, if one can twist the Jacobian of a curve by an element of its Brauer group, then probably this is the twist you need.