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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
comment Example of linearization for GIT
No! In the first case the answer is $V^\vee$, while in the second it is $V$.
Jul
21
comment 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.