Calabi-Yau differential operator database v.3.0

Summary

You searched for: inst=-96

Your search produced 2 matches

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New Number: 2.17 | AESZ: 111 | Superseeker: 32 1440 | Hash: d8535e0f3d0bfd4ebcc9c042df43c218

Degree: 2

$\theta^4-2^{4} x(2\theta+1)^2(8\theta^2+8\theta+3)+2^{12} x^{2}(2\theta+1)^2(2\theta+3)^2$

Coefficients of the holomorphic solution: 1, 48, 5904, 940800, 169520400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 32, -96, 1440, 19704, -14496, ... ; Common denominator:...

Discriminant

$(256z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 2}$
$0$ $1$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(\frac{ 1}{ 2}\)	\(\frac{ 1}{ 2}\)
\(0\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 2}\)
\(0\)	\(1\)	\(\frac{ 3}{ 2}\)

Note:

B-Incarnations:
Fibre product 81111- x 18--21, 4*11-- x 53211,
Double Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

New Number: 8.13 | AESZ: 163 | Superseeker: 12 3020/3 | Hash: e21fd830a9dca03305deb8363a26fcf2

Degree: 8

$\theta^4-2^{2} 3 x\left((3\theta^2+3\theta+1)^2\right)+2^{4} 3^{2} x^{2}\left(21\theta^4+156\theta^3+219\theta^2+126\theta+29\right)+2^{7} 3^{4} x^{3}(3\theta^2+3\theta+1)(3\theta^2-21\theta-35)-2^{10} 3^{5} x^{4}\left(27\theta^4+54\theta^3-114\theta^2-141\theta-49\right)+2^{12} 3^{7} x^{5}(3\theta^2+3\theta+1)(3\theta^2+27\theta-11)+2^{14} 3^{8} x^{6}\left(21\theta^4-72\theta^3-123\theta^2-72\theta-13\right)-2^{17} 3^{10} x^{7}\left((3\theta^2+3\theta+1)^2\right)+2^{20} 3^{12} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 180, 2352, 6084, ...
--> OEIS
Normalized instanton numbers (n₀=1): 12, -96, 3020/3, -71493/4, 319584, ... ; Common denominator:...

Discriminant

$(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2$

Local exponents

$-\frac{ 1}{ 72}\sqrt{ 6}$ $0$ $\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I$ $\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I$ $\frac{ 1}{ 72}\sqrt{ 6}$ $\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$ $\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $0$ $1$ $1$ $1$ $1$ $1$ $1$
$3$ $0$ $1$ $1$ $3$ $1$ $1$ $1$
$4$ $0$ $2$ $2$ $4$ $2$ $2$ $1$

\(-\frac{ 1}{ 72}\sqrt{ 6}\)	\(0\)	\(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\)	\(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\)	\(\frac{ 1}{ 72}\sqrt{ 6}\)	\(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)	\(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(3\)	\(0\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(4\)	\(0\)	\(2\)	\(2\)	\(4\)	\(2\)	\(2\)	\(1\)

Note:

Hadamard product $d \ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

\(-\frac{ 2}{ 3}+96\lambda\)	\(48\lambda\)	\(-\frac{ 5}{ 72}+4\lambda\)	\(-.13526746e-1\)
\(-\frac{ 2}{ 3}\)	\(\frac{ 2}{ 3}\)	\(-\frac{ 1}{ 36}\)	\(-\frac{ 5}{ 72}-4\lambda\)
\(-8\)	\(0\)	\(\frac{ 2}{ 3}\)	\(-48\lambda\)
\(-16\)	\(-8\)	\(-\frac{ 2}{ 3}\)	\(-\frac{ 2}{ 3}-96\lambda\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(-1\)
\(0\)	\(0\)	\(0\)	\(1\)

\(\frac{ 5}{ 3}-96\lambda\)	\(\frac{ 2}{ 3}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(\frac{ 2}{ 3}\)	\(0\)	\(-1\)	\(0\)
\(8\)	\(-16\)	\(0\)	\(0\)
\(16\)	\(0\)	\(0\)	\(0\)