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visits | member for | 4 years, 6 months |
seen | 9 hours ago | |
stats | profile views | 5,678 |
Sep 12 |
awarded | Civic Duty |
Sep 11 |
comment |
When are induction and coinduction of representations of Lie groups isomorphic? When they are compact? Semisimple?
@Turion: Of course. What I mean is that Dan in his answer implicitely identifies the category of representations with the category of sheaves on $BG$. But since he does not mention which sheaves are those, it is not clear which condition you really need. |
Sep 11 |
comment |
When are induction and coinduction of representations of Lie groups isomorphic? When they are compact? Semisimple?
@Turion: The question is whether you identify representations of $G$ with constructible sheaves on $BG$, or with coherent sheaves on $BG$. |
Sep 10 |
comment |
When are induction and coinduction of representations of Lie groups isomorphic? When they are compact? Semisimple?
@Dan Petersen: I think the question is in which category are you working --- if this is the category of constructible sheaves, then properness is probably enough, but if it is the category of coherent sheaves then I think you need the canonical class to be trivial. |
Sep 10 |
comment |
When are induction and coinduction of representations of Lie groups isomorphic? When they are compact? Semisimple?
@Dan Petersen: Don't you also need the relative canonical class to be trivial? |
Sep 9 |
comment |
Blowing up along birational equivalent subvarieties
$H^n(X_i,Z) = H^n(X,Z) \oplus H^{n-2}(V_i,Z)$, so if you want them to be equal for the blowups, you should have an equality for the centers which is not necessary true if $V_1$ and $V_2$ are only birational. |
Sep 5 |
answered | Sheaf isomorphism $\mathcal{F}\rightarrow f_{\ast}f^{\ast}(\mathcal{F})$? |
Sep 3 |
comment |
composition of t-structures “par recollement”
Do you mean that you have a semiorthogonal decomposition with three components and a t-structure on each of them, and now you want to glue them in two different ways? |
Aug 21 |
comment |
Does projective duality preserve arithmetic-Cohen-Macaulay-ness?
And is there an example with $X$ smooth? |
Aug 21 |
answered | Hilbert scheme of a closed subscheme |
Aug 19 |
answered | Open subset of the moduli space of stable sheaves on a noetherian scheme |
Aug 5 |
answered | Serre functor of a subcategory (in particular parabolic category O) |
Jul 22 |
comment |
Example of linearization for GIT
When $\dim V > 2$ projective spaces ${\mathbb{P}}V$ and ${\mathbb{P}}V^\vee$ are not isomorphisc (just because representations $V$ and $V^\vee$ are not isomorphic). |
Jul 22 |
comment |
Basic questions on the Hilbert scheme/ Douady space
@semyon alesker: ams.org/bookstore-getitem/item=SURV-123-S |
Jul 21 |
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Example of linearization for GIT
No! In the first case the answer is $V^\vee$, while in the second it is $V$. |
Jul 21 |
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Example of linearization for GIT
The answer depends on your convention on what $\mathbb{P}V$ is --- it can be either the moduli space of 1-dimensional subspaces in $V$, or the moduli space of 1-dimensional quotient spaces. Both conventions are used, so it is better to specify what do you mean here. |
Jul 21 |
revised |
Basic questions on the Hilbert scheme/ Douady space
added 1 character in body |
Jul 21 |
answered | Basic questions on the Hilbert scheme/ Douady space |
Jul 16 |
answered | Smooth Affine algebras are Calabi-Yau |
Jul 13 |
comment |
Does the following object has a name in algebraic geometry?
A section of $O(D)\otimes O(1)$ can be thought of as a pencil of sections of $O(D)$. Then $D'$ is "the total space" of this pencil. If smooth, it is isomorphic to the blowup of $X$ in the base locus of the pencil. |