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visits | member for | 4 years, 5 months |
seen | Sep 3 '13 at 14:28 | |
stats | profile views | 2,679 |
Oct 23 |
awarded | Yearling |
Apr 11 |
awarded | Nice Question |
Mar 12 |
comment |
What are some triangulations of Grassmannians?
I have nothing against Schubert cells, but the attaching maps are very complicated. I would be just as interested in hearing about a regular cell complex structure as a triangulation, but it's easy to get from one to the other so I asked about triangulations. If you know a triangulation that refines the Schubert stratification, so much the better! |
Mar 12 |
asked | What are some triangulations of Grassmannians? |
Nov 16 |
awarded | Popular Question |
Oct 23 |
awarded | Yearling |
Oct 13 |
comment |
The highest root of an ADE quiver
I was a little off: a nontrivial irrep matches to O(-1) on a reduced P^1. The trivial irrep matches to the structure sheaf of the scheme-theoretic exceptional fiber, shifted by 1. More stuff like this available here arxiv.org/abs/math/9812016 |
Oct 12 |
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The highest root of an ADE quiver
There's an equivalence of derived categories (G-equivariant coherent sheaves on C^2) = (coherent sheaves on a minimal resolution of the Duval singularity). It sends a nontrivial irrep of G (supported at the origin in C^2) to the structure sheaf of a component of the exceptional fiber. I wonder which sheaf on C^2 corresponds to a skyscraper on a node in the exceptional fiber. Whatever it is it has maps to and from the irrep. |
Sep 26 |
answered | When is the derived category of representations of a finite poset equivalent to its opposite? |
Nov 17 |
comment |
When are the fibers of a resolution of singularities reduced?
The usual resolutions of the D_n, E_6, E_7, and E_8 surface singularities do not have reduced fibers. The multiplicity of a component is the coefficient in the maximal root of the corresponding simple root. |
Oct 24 |
awarded | Yearling |
Oct 10 |
awarded | Popular Question |
Jul 1 |
asked | Is endoscopy interesting in simply-laced cases? |
May 27 |
awarded | Nice Answer |
Nov 18 |
accepted | How often does suspension define an action of Z/2 on a category of module spectra? |
Nov 17 |
asked | How often does suspension define an action of Z/2 on a category of module spectra? |
Oct 28 |
comment |
What are some open problems in toric varieties?
Let $X$ be a complete toric variety, necessarily neither smooth nor projective. Is there a nontrivial vector bundle on $X$? Payne has constructed examples that have no one- or two-dimensional bundles, and constructing vector bundles of higher rank on these is still open. The "mirror" question is whether there exists a Lagrangian submanifold of $(\mathbb{C}^*)^n$ satisfying certain asymptotic conditions coming from the fan of $X$. |
Oct 26 |
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Sheaves without global sections
But the condition that Frob is an isomorphism on H^i(X,O) is much weaker than being Frobenius split, like Torsten's example of a generic hypersurface. By now, does the opposite question look more interesting? On which varieties does every vector bundle have cohomology? |
Oct 26 |
comment |
Sheaves without global sections
Good lord I've been trying to make precisely that computation for like 90 minutes. For a del Pezzo surface it works because H^i(X,O) vanishes for i > 0. Are there "supersingular K3s" on which Frob:H^2(X,O) --> H^2(X,O) vanishes? |
Oct 25 |
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Sheaves without global sections
In characteristic p, you can try the cone on the map O --> Frob_* O. I'm confused about whether this works. |