Questions tagged [gromov-witten-theory]
The gromov-witten-theory tag has no usage guidance.
163 questions
1
vote
0
answers
151
views
Is Gromov-Witten theory of Calabi-Yau threefolds of Type A trivial?
There are some Calabi-Yau threefolds that do not contain any rational curves, e.g. Calabi-Yau threefold of type A in the paper "Calabi-Yau threefolds of quotient type" by Oguiso and Sakurai.
My ...
- 11
2
votes
1
answer
643
views
Computing 3 points Gromov-Witten invariants of the Grassmannian
This is from an exercise in Koch, Vainsencher - An invitation to quamtum cohomology.
Background
The exercise asks to compute the 3-points Gromov-Witten invariants of the Grassmannian $G = \mathop{Gr}...
- 14.8k
7
votes
0
answers
582
views
Gromov-Witten invariants of singular spaces
I wonder if there is any situation where one can talk about Gromov-Witten invariants
or quantum multiplication for singular varieties. Ideally, I would like have a situation
where for a singular ...
- 7,037
4
votes
2
answers
757
views
Convergence of quantum cohomology
For which manifolds or varieties is quantum cohomology known to converge? Are there any manifolds for which quantum cohomology is known to not converge? I seem to have the impression that quantum ...
- 21k
2
votes
0
answers
761
views
a question on Costello's theorem
Costello's theorem,"open TCFT=Calabi Yau A-infinity category",he also mentions when applied to Fukaya category we can recover Gromov-Witten theory, but I see that it needs some assumption,also even if ...
- 1,499
3
votes
0
answers
369
views
genus one Gromov-Witten invariants of Calabi-Yau 3-folds
In
http://arxiv.org/PS_cache/hep-th/pdf/9302/9302103v1.pdf
physicists calculate (predict) genus one GW invariants of quintic (Table 1) and some other cases (Table 2).
Can any body explain to me (...
3
votes
0
answers
247
views
Transitive action on moduli space of holomorphic curves.
If $G$ is a complex semi simple Lie group and $P$ is a parabolic subgroup of it, the quotient $G/P$ is endowed with a Kahler structure and the action of $G$ on $G/P$ is holomorphic with respect to ...
- 31
2
votes
1
answer
385
views
What's the chain level Gromov-Witten theory
I think I heard there is such a theory, but I just can't find reference.So I am asking if there really has such a theory and reference if yes. Thanks firstly!
- 1,499
2
votes
0
answers
174
views
Are there ways to make low degree checks for enumerative formulas except for curves in CP^2?
This is a concrete question in Enumerative geometry. Let $S$ be a compact
complex surface and $L\rightarrow S$ a holomorphic line bundle. Let
$$ \delta_d = \text{dim}~ \mathbb{P}(H^0(S,L^d)) $$
...
- 3,245
3
votes
1
answer
249
views
GW invariants for varieties with negative first Chern class
Does there exist any theorem claiming that if a variety with negative first Chern class has no rational curves then every GW invariant is zero?
4
votes
0
answers
202
views
The hypergeometric pullback conjecture
Here arXiv:math/0510287, Golishev proposed the following conjecture:
The hypergeometric pullback conjecture. Let $X$ be a Fano variety. Then,for any constituent $C$ of the quantum D-module $Q$ there ...
5
votes
0
answers
280
views
Gromov-Witten theory of equivariant local projective plane
Can I find written explicitly in the literature a formula for the genus zero equivariant Gromov-Witten theory of local $\mathbb{P}^2$?
I understand that the method of Givental will give the answer, ...
- 8,723
0
votes
0
answers
140
views
Obstruction theories on non-smooth spaces with smooth fibres
Given a perfect obstruction theory $E^\bullet$ over a space $X$, we know that if $X$ is smooth, that the virtual fundamental class $[X, E^\bullet]$ is given by
$$[X, E^\bullet] = c_{top}\big((E^{-1})^...
- 6,290