Calabi-Yau differential operator database v.3.0

1

New Number: 2.25 | AESZ: 138 | Superseeker: 27 2618 | Hash: c524254b716132352b27914640b03c8b

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...

Discriminant

$(243z-1)(216z-1)$

Local exponents

$0$ $\frac{ 1}{ 243}$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 243}\)	\(\frac{ 1}{ 216}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast g$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(108\)	\(36\)	\(15\)

2

New Number: 5.1 | AESZ: 17 | Superseeker: 6/5 118/5 | Hash: 370d10edbf5900002f79cf6163e106a5

Degree: 5

$5^{2} \theta^4-3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2 3 x^{2}\left(531\theta^4+828\theta^3+541\theta^2+155\theta+15\right)-2 3^{3} x^{3}\left(423\theta^4+2160\theta^3+4399\theta^2+3795\theta+1170\right)+3^{5} x^{4}\left(279\theta^4+1368\theta^3+2270\theta^2+1586\theta+402\right)-3^{10} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 3, 27, 381, 6219, ...
--> OEIS
Normalized instanton numbers (n₀=1): 6/5, 39/10, 118/5, 1443/10, 6108/5, ... ; Common denominator:...

Discriminant

$-(27z-1)(27z^2+1)(-5+9z)^2$

Local exponents

$0-\frac{ 1}{ 9}\sqrt{ 3}I$ $0$ $0+\frac{ 1}{ 9}\sqrt{ 3}I$ $\frac{ 1}{ 27}$ $\frac{ 5}{ 9}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $1$
$1$ $0$ $1$ $1$ $1$ $1$
$1$ $0$ $1$ $1$ $3$ $1$
$2$ $0$ $2$ $2$ $4$ $1$

\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)	\(0\)	\(0+\frac{ 1}{ 9}\sqrt{ 3}I\)	\(\frac{ 1}{ 27}\)	\(\frac{ 5}{ 9}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(3\)	\(1\)
\(2\)	\(0\)	\(2\)	\(2\)	\(4\)	\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 290/5.71
A-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \times P^2 \times P^2$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-90\)	\(108\)	\(90\)	\(24\)

3

New Number: 5.81 | AESZ: 312 | Superseeker: 5/7 48/7 | Hash: 767262575f8b1458839c1e9a8beacf0a

Degree: 5

$7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...

Discriminant

$(16z+1)(2z-1)(27z-1)(7+26z)^2$

Local exponents

$-\frac{ 7}{ 26}$ $-\frac{ 1}{ 16}$ $0$ $\frac{ 1}{ 27}$ $\frac{ 1}{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 5}{ 6}$
$1$ $1$ $0$ $1$ $1$ $1$
$3$ $1$ $0$ $1$ $1$ $1$
$4$ $2$ $0$ $2$ $2$ $\frac{ 7}{ 6}$

\(-\frac{ 7}{ 26}\)	\(-\frac{ 1}{ 16}\)	\(0\)	\(\frac{ 1}{ 27}\)	\(\frac{ 1}{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 5}{ 6}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "5.81" from ...

\(.84386396e-1+.881341465I\)	\(-.593907697+1.816219110I\)	\(.987405021+.251865740I\)	\(-.18197034e-1-.280246794I\)
\(-.610146073+4.105015738I\)	\(3.086102688+5.881005017I\)	\(\frac{ 1}{ ln}(2)^{ \frac{ 8}{ 3}}ln(3)^{ \frac{ 8}{ 5}}Zeta(5)^8-1.317777791I\)	\(-.605925748-.688412508I\)
\(-1.084750363+4.722447485I\)	\(1.891556916+7.035664131I\)	\(4.676916900-1.255046419I\)	\(-.642466556-.856579334I\)
\(-4.881168587+32.840125900I\)	\(16.688821505+47.048040140I\)	\(24.445126799-10.542222328I\)	\(-3.847405984-5.507300063I\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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

\(1.+.755979502I\)	\(0\)	\(\frac{ 39}{ 2}\lambda\)	\(.15875139e-1\)
\(\frac{ 9}{ 2}\)	\(1\)	\(\frac{ 9}{ 16}\)	\(-\frac{ 39}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(36\)	\(0\)	\(\frac{ 9}{ 2}\)	\(1.-.755979502I\)

\(-\frac{ 377989751}{ 500000000}I\)	\(\frac{ 21}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 9}{ 2}\)	\(-18\)	\(-1\)	\(0\)
\(0\)	\(36\)	\(0\)	\(0\)
\(-36\)	\(0\)	\(0\)	\(0\)