Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with ag.algebraic-geometry
Search options not deleted
user 1703
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
13
votes
Accepted
Complex torus, C^n/Λ versus (C*)^n
The difference between an Abelian variety and $\mathbb{C}^n/\Lambda$ is that an abelian variety is polarized; that is, it comes with an ample line bundle, which yields an embedding into $\mathbb{P}^m$ …
- 6,242
10
votes
1
answer
286
views
What can we say about tropical maps $\mathbb{P}^1 \to A$ for an Abelian variety $A$?
It's well known that maps $\mathbb{P}^1_\mathbb{C} \to A$ are constant for any Abelian variety $A$ (in fact, for any complex torus).
Is there any similar statement in the tropical case? Naively, the …
- 6,242
1
vote
Ramification of the map from the stack of elliptic curves to the $j$-line
I would guess that the following argument should work.
By definition, the map $\mathbb{H} \to \mathcal{M}_{1,1} = [SL_2\mathbb{Z} \setminus \mathbb{H}]$ is unramified. However, the map $\mathbb{H} \t …
- 6,242
5
votes
Accepted
Meaning of $g_d^r$ in algebraic geometry
As I understand, a $g_d^r$ is a linear system of dimeansion $r$ and degree $d$. Basically, these give you maps to $\mathbb{P}^r$ of degree $d$. The simplest example is of course hyperelliptic curves; …
- 6,242
9
votes
3
answers
951
views
Is there an intrinsic way to define the group law on Abelian varieties?
On an elliptic curve given by a degree three equation y^2 = x(x - 1)(x - λ), we can define the group law in the following way (cf. Hartshorne):
We note that the map to its Jacobian given by $\mathca …
- 6,242
2
votes
2
answers
872
views
What is the difference between the moduli space of curves and the moduli space of orbi-curves?
Edit: In my original framing of this question it was not so clear what I was looking for, so this is basically a re-write.
I feel that I should already know the answer to this, but it never sits quit …
- 6,242
8
votes
What is the meaning of non-Hausdorff spaces in algebraic geometry
One of the things to think about in Algebraic Geometry is that the natural topology (Zariski topology) is the wrong topology, at least in part for the reasons you describe. There are other "topologies …
- 6,242
56
votes
3
answers
8k
views
What are the benefits of viewing a sheaf from the "espace étalé" perspective?
I learned the definition of a sheaf from Hartshorne—that is, as a (co-)functor from the category of open sets of a topological space (with morphisms given by inclusions) to, say, the category of sets. …
- 6,242
12
votes
Elliptic curves on abelian surface
No. In general, there are no elliptic curves on an Abelian surface.
Thinking in terms of lattices, if there is an elliptic curve on $A$, then there is a rank 2 sublattice of $\Lambda$ (Where $A = \m …
- 6,242
0
votes
Describing the kernel of the exponential map as a homology group
This morally sounds like it should be related to the exponential sequence in sheaf cohomology, but I don't immediately see how... Although, absent the torus (which I take as meaning $(\mathbb{C}^\time …
- 6,242
5
votes
Accepted
$\psi$ class in $\overline{M}_{0,n}$
Unless you mean something else when you write $\psi$ class, it is expressible in terms of boundary divisors.
That is, if $\psi_i$ is the $i$-th cotangent bundle, then you can write it in terms of bou …
- 6,242
2
votes
on a Deformation long exact sequence of moduli space of stable maps
I don't believe that this is correct. The easiest way to see this is to look at your second question: The automorphisms/deformations/obstructions of a curve come from $H^i(C, T_C)$, i.e. they are the …
- 6,242
9
votes
1
answer
259
views
How is the propagator computed on an elliptic curve?
I've been struggling for a while now understanding why the propagator for the action
$$
S(\varphi) = \int_E \partial \varphi \bar\partial\varphi + \frac{\lambda}{6}(\partial\varphi)^3
$$
on an ellipti …
- 6,242
3
votes
What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
The comment by user76758 hits the nail pretty much perfectly on the head. That said, it might be good to see an example of something that does not satisfy this condition:
Let $X$ be any scheme, and l …
- 6,242
8
votes
0
answers
384
views
Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s
It is well known (cf. Dolgachev) that there is a beautiful notion of mirror symmetry for lattice-polarized K3 surfaces. That is, if we are given a rank $r$ lattice $M$ of signature $(1, r - 1)$ and a …
- 6,242