All Questions
Tagged with gromov-witten-theory reference-request
11 questions
12
votes
3
answers
3k
views
References for Donaldson-Thomas theory and Pandharipande-Thomas theory?
I'm looking for good introductory references for Donaldson-Thomas theory and Pandharipande-Thomas theory. I know a bit about Gromov-Witten theory, but almost nothing about Donaldson-Thomas and ...
- 21k
7
votes
1
answer
299
views
Gromov-Witten invariants and the mod 2 spectral flow
I'm reading Lee-Parker, “A structure theorem for the Gromov-Witten invariants of Kähler
surfaces”, which studies Gromov-Witten invariants within symplectic
geometry. Lee-Parker write (&...
- 6,881
6
votes
1
answer
366
views
Toda Hierarchy and Quantum Cohomology of $\mathbb{P}^1$ Frobenius manifolds
People usually say that the quantum cohomology of $\mathbb{P}^1$ Frobenius manifold $QH^*(\mathbb{P}^1)$, corresponds to dispersionless extended Toda hierarchy (e.g. page 6 of https://arxiv.org/pdf/...
- 425
5
votes
0
answers
372
views
Deformation theory with a view toward GW theory and DT theory
I am studying GW theory (and DT theory) in algebraic geometry. I now understand the heuristic "Aut, Def, Obs" argument written in Mirror Symmetry book (by Hori et al.), but it is too hard for me to ...
- 349
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
4
votes
2
answers
957
views
Explicit computation of Gromov-WItten invariants
After studying some foundation of Gromow-Witten invariants, I now would like to see an explicit computation. I heard that one should first take a look at the total space of $\mathcal{O}(-1)^{\oplus2}$ ...
- 241
2
votes
1
answer
624
views
Reference request for Gromov-Witten Invariants of non compact manifolds
The title of my question essentially explains what I am looking for, but let elaborate a bit, to put it in a more specific context.
There are quite a few papers, where the authors compute Gromov-...
- 3,245
2
votes
0
answers
181
views
Is there a degeneration formula for Gromov-Witten K-theoretic invariants?
By Gromov-Witten K-theoretic invariants (call them KGW) I mean the invariants defined by Givental and Lee.
I expect the formula expresses the KGW of the generic fiber of a given degeneration in terms ...
- 21
2
votes
0
answers
206
views
Are rational varieties symplectically rationally connected?
Was it proven already that smooth rational complex projecitve varieties are symplectically rationally connected? I.e. some GW invariant with two point insertions is non zero. What about smooth toric ...
- 14.3k
1
vote
0
answers
122
views
Is it possible to find an explicit definition of the "universal" (co)tangent bundle?
Let $H_{0,1}(\mathbb{P}^2, d)$ be the space of holomorphic degree $d$
maps (that are not multiply covered) from $\mathbb{P}^1$ to $\mathbb{P}^2$ with one marked point
$y \in \mathbb{P^1} $ $\textit{...
- 3,245
0
votes
0
answers
231
views
Is the complex structure on a del-Pezzo surface a regular complex structure?
Let $(X, \omega, J)$ be a compact symplectic manifold with an almost complex structure. Fix some homology class $\beta \in H_2(X, \mathbb{Z})$. An almost
complex structure $J$ is said to be $\textit{...
- 3,245