All Questions
Tagged with enumerative-geometry gromov-witten-theory
9 questions with no upvoted or accepted answers
9
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Question on Ionel and Parker's paper: Relative Gromov Witten Invariants
In defining Gromov-Witten invariants using symplectic geometry, most of the trouble is to achieve transversality for moduli spaces of pseudo-holomorphic curves which are multiple covers of simple ones....
- 1,331
4
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How does one obtain the formula for the number of genus one curves in P^2 using Getzler's relation?
I am trying to get the formula for the number of degree $n$ genus one curves in $\mathbb{P}^2$ passing through 3n generic points, by following the procedure in Getzler's paper
https://arxiv.org/pdf/...
- 3,245
3
votes
0
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165
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Enumerative or Gromov-Witten invariants from derived category of coherent sheaves
Let $X$ be a smooth projective toric Fano surface over $\mathbb{C}$. Suppose I have a nice presentation of $D^b_{Coh}(X)$ given by a full, strong exceptional collection $\mathcal{E} = \{E_i\}_{i\in I}$...
- 511
3
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holomorphic embeddings of the sphere into the quintic in degree 2
Is there an explicit way of
classifying (with regard to their compatibiliy with $\Omega_+$ or $\Omega_-,$ see below)
the various families of
equivariant holomorphic embeddings from $\mathbb{CP}^1$ to ...
2
votes
0
answers
99
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Diagonal operator and infinite wedge space formalism
Let $\bigwedge^{\infty /2}V$ denote semiinfinte wedge space. The followin article section 2 gives a good description about the space and the operator on it.
https://arxiv.org/pdf/math/0207233.pdf
...
- 685
2
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0
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162
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Degree 2 curves on a degree d hypersurface in P^(2d+2)/3
One of the foundations of Gromov-Witten theory is the use (due to Kontsevich I think) of localization to calculate the number of degree $n$ curves on a general quintic 3-fold. When calculating the ...
- 265
2
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0
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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
1
vote
0
answers
241
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De Jonquières formula vs. Relative GW invariants
Background. Let $C$ be a smooth projective curve of genus $g$. Denote by $C^d$ its d-th symmetric product and by $G^r_d(C)$ its associated variety
of linear series of type $\mathfrak{g}^r_d$, i.e.
$$ ...
- 1,981
1
vote
0
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266
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How does one define Moduli spaces in Symplectic Geometry and naively interpret higher genus GW Invariants?
This is a very basic question about the definition of Moduli space of maps.
My reason for asking this question is because I haven't actually seen this
definition explicitly given anywhere, and hence ...
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