New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(7\theta^2+7\theta+2)-2^{3} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ... --> OEIS Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...
Discriminant
\(-(27z+1)(216z-1)\)
Local exponents
Note:
Hadamard product $B\ast a$.
A-Incarnation: diagonal of (3,3)-intersection in $P^2 \times P^2$
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 21, 3861, 429159, 57224661, 7337893896, 968171025159, 128100057340668,...
Coefficients of the q-coordinate : 0, 1, -48, -18, 7976, -1697115, -90056880, -9049527514,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}\dbinom{n}{k}^3\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(4+324\lambda\) | \(-\frac{ 3}{ 2}-162\lambda\) | \(\frac{ 3}{ 4}+81\lambda\) | \(-\frac{ 222}{ 1223}-54\lambda\) |
\(9\) | \(-\frac{ 7}{ 2}\) | \(\frac{ 9}{ 4}\) | \(-\frac{ 3}{ 4}-81\lambda\) |
\(18\) | \(-9\) | \(\frac{ 11}{ 2}\) | \(-\frac{ 3}{ 2}-162\lambda\) |
\(36\) | \(-18\) | \(9\) | \(-2-324\lambda\) |
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 \(1+162\lambda\) | \(0\) | \(27\lambda\) | \(.34239575e-1\) |
\(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(-27\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(18\) | \(0\) | \(3\) | \(1-162\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-162\lambda\) | \(6\) | \(1\) | \(1\) |
\(-3\) | \(-9\) | \(-1\) | \(0\) |
\(0\) | \(18\) | \(0\) | \(0\) |
\(-18\) | \(0\) | \(0\) | \(0\) |
copy data