Reputation
7,266
Next privilege 10,000 Rep.
Access moderator tools
Badges
4 61 126
Impact
~314k people reached

Apr
26
comment Definitions of Hilbert Bundles
@TanujD., Yes, coherent sheaves (and their possibly "infinite dimensional" cousins, quasicoherent sheaves) have sections, which form vector spaces. But I don't think looking directly into the algebraic geometry literature would be the most sensible path... Maybe there is something analogous to QC sheaves in the noncommutative geometry literature?
Apr
26
comment Definitions of Hilbert Bundles
Only slightly related but: in algebraic/holomorphic geometry you have coherent sheaves that are pretty much like vector bundles in which the dimension of fibers can jump (in an upper semi-continuous way, in this case), and they are as "natural" objects as bundles are.
Apr
23
awarded  Popular Question
Apr
19
revised A Hartogs-type criterion for flatness
(name)
Apr
15
awarded  Popular Question
Apr
13
awarded  Nice Answer
Apr
13
revised Is there a way to graphically imagine smash product of two topological spaces?
deleted 8 characters in body
Apr
11
accepted Is locally freeness of a sheaf (of fixed rank) around a divisor detectable from a first order neighbourhood?
Apr
9
comment Is locally freeness of a sheaf (of fixed rank) around a divisor detectable from a first order neighbourhood?
Thank you for your answer!
Apr
8
asked Is locally freeness of a sheaf (of fixed rank) around a divisor detectable from a first order neighbourhood?
Apr
5
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
Thank you for the reference.
Apr
4
comment Equivariant Riemann-Roch on DM stacks?
I have an action of a torus on an orbifold surface $X$, and I want to compute the induced weights on the $Ext^1$ of two invariant sheaves (assuming I know those on the $Ext^0$ and on the $Ext^2$). It would be perhaps useful to have (if it exists) a formula like $Ext^0(E,F)-Ext^1(E,F)+Ext^2(E,F)=\int_X ch^{\vee}(E)ch(F)Td(X)$. The equality is supposed to hold in the representation ring of the torus, or in some other setting that can help computing the LHS..
Apr
3
asked Equivariant Riemann-Roch on DM stacks?
Apr
3
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
Ok, I see. Thank you all for your comments.
Apr
3
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
For which reason does the presence of an infinite stratification on a finite dim stack prevent the functor of isom classes from having a (possibly badly non separated) coarse moduli space?
Apr
3
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
Just to understand: what is the dimension of the connected component of the trivial bundle in the stack? and what is the dimension of the biggest stabilizer (I would say $n^2$)?
Apr
2
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
Also, does the functor of isomorphism classes have a coarse moduli space? (still talking of GL(n) )
Apr
2
comment Moduli space of (all) vector bundles on $\mathbb{P}^1$
But, in the case of $GL(n)$, doesn't Grothendieck 's theorem imply some sort of "discreteness"? For example, does every connected component of $Bun_n(\mathbb{P}^1$ have a unique closed point? What is the dimension of such components anyway (upon, say, also fixing the degree of bundles)? If this turns out to be minus the dimension of its generic stabilizer, for example, I would count this as some sort of -quotes- "discreteness" property...
Apr
1
asked Moduli space of (all) vector bundles on $\mathbb{P}^1$
Mar
23
comment No matter how many algebraic invariants we attach to topological spaces, there will always be nonhomeomorphic spaces agreeing on all their invariants
Also relevant is the answer to: mathoverflow.net/questions/21667/…