New Number: 2.6 | AESZ: 24 | Superseeker: 36 41421 | Hash: 5e8f8f32b5e99693a2956e1240b9fdff
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(11\theta^2+11\theta+3)-3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 18, 1710, 246960, 43347150, ... --> OEIS Normalized instanton numbers (n0=1): 36, 837, 41421, 2992851, 266362506, ... ; Common denominator:...
Discriminant
\(1-297z-729z^2\)
Local exponents
Note:
Hadamard product B*b
Related to
7.19,
8.18This operator corresponds to $(Grass(2,5)\vert 1,1,3)_{-150}$ from
arXiv:0802.2908Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 36, 6732, 1118403, 191549196, 33295313286, 5856252011883, 1038763114502247,...
Coefficients of the q-coordinate : 0, 1, -75, 1539, -60073, -2978346, -380743659, -48420276097,...
| Gopakumar-Vafa invariants |
|---|
| g=0 | 540, 12555, 621315, 44892765, 3995437590, 406684089360, 45426958360155, 5432556927598425,... |
| g=1 | 0, 0, -1, 13095, 17230617, 6648808835, 1831575868830, 433375127634753,... |
| g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{n+k}{n}\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
| \(\frac{ 11}{ 2}+600\lambda\) | \(-\frac{ 9}{ 4}-300\lambda\) | \(\frac{ 21}{ 20}+140\lambda\) | \(-.196596398-90\lambda\) |
| \(14\) | \(-6\) | \(\frac{ 49}{ 15}\) | \(-\frac{ 21}{ 20}-140\lambda\) |
| \(30\) | \(-15\) | \(8\) | \(-\frac{ 9}{ 4}-300\lambda\) |
| \(60\) | \(-30\) | \(14\) | \(-\frac{ 7}{ 2}-600\lambda\) |
copy data | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 6}\) |
| \(0\) | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(0\) | \(1\) | \(-1\) |
| \(0\) | \(0\) | \(0\) | \(1\) |
copy data | \(1+150\lambda\) | \(0\) | \(\frac{ 55}{ 2}\lambda\) | \(.35225900e-1\) |
| \(\frac{ 11}{ 4}\) | \(1\) | \(\frac{ 121}{ 240}\) | \(-\frac{ 55}{ 2}\lambda\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(15\) | \(0\) | \(\frac{ 11}{ 4}\) | \(1-150\lambda\) |
copy data Basis of the Doran-Morgan lattice
| \(-150\lambda\) | \(\frac{ 21}{ 4}\) | \(1\) | \(1\) |
| \(-\frac{ 11}{ 4}\) | \(-\frac{ 15}{ 2}\) | \(-1\) | \(0\) |
| \(0\) | \(15\) | \(0\) | \(0\) |
| \(-15\) | \(0\) | \(0\) | \(0\) |
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