Calabi-Yau differential operator database v.3.0

Summary

You searched for: h3=96

Your search produced 2 matches

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New Number: 5.6 | AESZ: 23 | Superseeker: 4/3 44/3 | Hash: 65760d446ba9c3da587ce5bd9912745e

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...

Discriminant

$-(-1+32z)(16z-1)^2(32z-3)^2$

Local exponents

$0$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 16}$ $\frac{ 3}{ 32}$ $\infty$
$0$ $0$ $0$ $0$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $3$ $1$
$0$ $2$ $1$ $4$ $1$

\(0\)	\(\frac{ 1}{ 32}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 3}{ 32}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(3\)	\(1\)
\(0\)	\(2\)	\(1\)	\(4\)	\(1\)

Note:

There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9
A-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \times P^4$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-32\)	\(96\)	\(96\)	\(24\)

New Number: 8.14 | AESZ: 176 | Superseeker: 24 15448/3 | Hash: e2a40a57f7e88dba6655d936b4abe327

Degree: 8

$\theta^4-2^{2} x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{5} x^{2}\left(325\theta^4+2164\theta^3+3053\theta^2+1778\theta+420\right)+2^{10} 3^{2} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{14} 3^{2} x^{4}\left(397\theta^4+794\theta^3-1454\theta^2-1851\theta-666\right)+2^{18} 3^{4} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{21} 3^{4} x^{6}\left(325\theta^4-864\theta^3-1489\theta^2-864\theta-144\right)-2^{26} 3^{6} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{32} 3^{8} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 840, 34944, 1618344, ...
--> OEIS
Normalized instanton numbers (n₀=1): 24, -509/2, 15448/3, -128530, 3746624, ... ; Common denominator:...

Discriminant

$(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2$

Local exponents

$-\frac{ 1}{ 48}$ $0$ $\frac{ 1}{ 72}$ $\frac{ 1}{ 64}$ $\frac{ 1}{ 48}$ $\frac{ 1}{ 36}$ $\frac{ 1}{ 32}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $0$ $1$ $1$ $1$ $1$ $1$ $1$
$3$ $0$ $1$ $1$ $3$ $1$ $1$ $1$
$4$ $0$ $2$ $2$ $4$ $2$ $2$ $1$

\(-\frac{ 1}{ 48}\)	\(0\)	\(\frac{ 1}{ 72}\)	\(\frac{ 1}{ 64}\)	\(\frac{ 1}{ 48}\)	\(\frac{ 1}{ 36}\)	\(\frac{ 1}{ 32}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(3\)	\(0\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(4\)	\(0\)	\(2\)	\(2\)	\(4\)	\(2\)	\(2\)	\(1\)

Note:

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

Calabi-Yau differential operator database v.3

Summary

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