a*t^3 + (2*a-b)*t^4 + a*t^5
= a*t^3*(1+t)^2 - (a+b)*t^4

[1,1,2,3,3,10],
d:=10; A:=[1,1,2,3,3]; B:=[[]];
D := P(d,A) - PA(A);
D*&*[1-t^i : i in [1,1,3,3]];  // 2*t^5 + t^4 + 2*t^3
  // a = 2, b = 1;
  // the 1 eigensheaf is gen by x1, x2 mod x1*cubic + x2*cubic = 0
  // -> it is 2 Oh(-1)/Oh(-10) = Oh(8) ??
  // the 2 eigensheaf is gen by y -> (OhGa(-2)) ??
  // E1 = Oh(-1,-1,+10) = Oh(8), E2 = Oh(-2), E1-E2 = 10, deg = 6*a-2*b
curve Ga of 1/3(1,2). Contr sum of two components 1/3(1) and 1/3(2)?
  // 

[1,1,3,3,5,13],
d:=13; A:=[1,1,3,3,5]; B:=[[5,1,1,3]];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,3]]; // 3*t^5 + 2*t^4 + 3*t^3

curve Ga of 1/3(1,2); same deg = 1/(3*3) as previous case. Contr sum of
two components 1/3(1) and 1/3(2)?
  // a = 3, b = 1. E1 = Oh(11), E2 = Oh(-5)
  // E1 = Oh(11), E2 = Oh(-5), E1-E2 = Oh(16), deg = 6*a-2*b

[1,1,3,3,8,16],
d:=16; A:=[1,1,3,3,8]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,3]]; // 4*t^5 + 3*t^4 + 4*t^3
  // a = 4, b = 3. E1 = Oh(14), E2 = Oh(-8), E1-E2 = Oh(22), deg = 6*a-2*b

curve Ga of 1/3(1,2); same deg = 1/(3*3) as previous cases. Contr sum of
two components 1/3(1) and 1/3(2)?
  2 -> 5 -> 8 adds t^3+t^4+t^5; increasing some deg of 2 compt

[1,1,3,6,8,19],
d:=19; A:=[1,1,3,6,8]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - 1/(6*8)*Phalfc() - Pemb2(4);
D*&*[1-t^i : i in [1,1,3,3]];
  This has a curve Ga2 of 1/2 with emb 1/6(1,3,2) and 1/8(1,1,6)
  and Ga3 of 1/3 with emb 1/6(1,3,2)

[1,1,3,9,14,28], // emb 1/9(1,3,14)
d:=28; A:=[1,1,3,9,14]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,9]];
  // 3*t^11+3*t^10+4*t^9+3*t^8+3*t^7+3*t^6+4*t^5+3*t^4+3*t^3

[1,2,2,3,3,11],
d:=11; A:=[1,2,2,3,3]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*2)*Phalfc();
D*&*[1-t^i : i in [1,1,3,3]]; // -t^5 - 2*t^4 - t^3
  // a = -1, b = -2
  // E1 = Oh(-1), E2 = Oh(7), E1-E2 = -8, deg = 6*a-2*b

[1,2,3,3,8,17]
d:=17; A:=[1,2,3,3,8]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*8)*Phalfc() - c8233;
  // it's 1/8(2,3,3) not (1,1,6) // -t^5 - 2*t^4 - t^3
  // a = -1, b = -2
  // E1 = Oh(-1), E2 = Oh(-2,-8+17) so Oh(7). E1-E2 = -8, deg = 6*a-2*b

========= digress to get c8233
[2,2,3,3,8,18],
d := 18; A:=[2,2,3,3,8]; B:= [[3,2,2,2] : i in [1..6]];
D := P(d,A) - PA(A) - Pb(B) - 18/(2*2*8)*Phalfc();

c8233 := - 9/16*Phalfc() + (t^8-2*t^7+3*t^6-2*t^5+t^4)/&*[1-t^i : i in [1,1,2,8]];

 P(d,A) eq PA(A) + Pb(B)  + 18/(2*2*8)*Phalfc() + c8233; // true


[1,2,2,3,6,14],
[1,2,2,6,9,20],
[1,2,3,3,3,12],
d:=12; A:=[1,2,3,3,3]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,3]]; // 2*t^5 - 2*t^4 + 2*t^3
 // The curve has deg 12/(3*3*3) = 4/9 = 4 times unit
 // a = 2, b = -2, a-b = 4;
 // E1 = Oh(-1), E2 = Oh(-2), E1-E2 = Oh(1), deg = 4,
 whereas 6*a-2*b = 10, genus = 3

[1,2,3,3,9,18],
d:=18; A:=[1,2,3,3,9]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,3]]; 
  // t^3-t^4+t^5
  // the curve has deg 18/(3*3*9) = 2/9
  // get the value 2*model above
  // a = 1, b = -1
  // E1 = Oh(-1), E2 = Oh(-2), E1-E2 = Oh(1), deg = 2,
  whereas 6*a-2*b = 4, genus = 2

[1,2,3,3,6,15],
[1,2,3,3,7,16],
d := 16; A := [1,2,3,3,7]; B := [[7,1,3,3]];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,3]]; // 2*t^5 + t^4 + 2*t^3
  E1 = Oh(8), E2 = Oh(-2), E1-E2 = Oh(10), deg = 6*a-2*b

[1,2,3,3,8,17],   // has 1/8(2,3,3)
d:=17; A:=[1,2,3,3,8]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*8)*Phalfc() - c8233;
D*&*[1-t^i : i in [1,1,3,3]]; // -t^5 - 2*t^4 - t^3
  E1 = Oh(-1), E2 = Oh(-2-8+17) = Oh(7), E1-E2 = Oh(-8), deg = 6*a-2*b

[1,2,3,4,6,16],
[1,2,3,4,9,19],
[1,2,3,5,9,20],
d := 20; A:=[1,2,3,5,9]; B:= [];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,9]]; // t^5 + t^9
  // emb 1/9(1,3,5)
 
[1,2,3,6,6,18],
 // 3 x 1/6(1,2,3)
d := 18; A := [1,2,3,6,6]; B := [];
D := P(d,A) - PA(A) - Pb(B) - 18/(2*6*6)*Phalfc() - 18/(3*6*6)*1/2*(t^3-t^4+t^5);

[1,2,3,6,9,21],

[1,2,3,6,10,22],
[1,2,3,6,11,23],
[1,2,3,6,12,24],
[1,2,3,9,12,27],
[1,2,3,9,13,28],
d := 28; A:=[1,2,3,9,13]; B := [[13,1,3,9]];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,9]];  // -t^9 + t^8 - t^7 + t^6 - t^5

[1,2,3,9,14,29],
[1,2,3,9,15,30],
d:=30; A:=[1,2,3,9,15]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
D*&*[1-t^i : i in [1,1,3,9]];  // t^6 - t^7 + t^8
 // Ga of deg 30/(3*9*15) with emb 1/9(1,2,6)

[1,2,3,12,18,36],
[1,2,4,9,12,28],
[1,2,4,9,15,31],
[1,2,6,6,9,24],
[1,2,6,6,15,30],
[1,2,6,8,15,32],
[1,2,6,9,9,27],
[1,2,6,9,12,30],
[1,2,6,9,18,36],
[1,2,6,10,17,36],
[1,2,6,12,15,36],
[1,2,6,12,21,42],
[1,2,6,15,22,46],
[1,2,6,15,23,47],
[1,2,6,18,27,54],

[2,2,3,3,7,17],
d:=17; A:=[2,2,3,3,7]; B := [[7,2,2,3]];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*2)*Phalfc();
 // -3*t^5 - 4*t^4 - 3*t^3
 // a = -3, b = -4
 // E2 = Oh(13), E1 = Oh(-7), E1-E2 = Oh(-20), deg = 6*a-2*b

[2,2,3,3,10,20],
d:=20; A:=[2,2,3,3,10]; B := [];
D := P(d,A) - PA(A) - Pb(B) - 20/(2*2*10)*Phalfc();
 // -4*t^5 - 5*t^4 - 4*t^3
 // a = -4, b = -5
 // E2 = Oh(16), E1 = Oh(-10), E1-E2 = Oh(-26), deg = 6*a-2*b
 
[2,2,3,6,7,20],
[2,2,3,6,13,26],
[2,2,3,9,14,30],
[2,2,3,14,21,42],

[1,3,3,3,5,15],
d:=15; A := [1,3,3,3,5]; B := [];
D := P(d,A) - PA(A) - Pb(B);
  // 5*(t^3 + t^5)/&*[1-t^i : i in [1,1,3,3]];
  // same deg = 5/(3*3)
  // a = 5, b = 0
  // E1 = Oh(-1), E2 = Oh(-5), E1-E2 = Oh(4), deg = 20,
  whereas 6*a-2*b = 28, g = 6.

[2,3,3,3,4,15]
d := 15; A := [2,3,3,3,4]; B := [];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*4)*Phalfc() - c4233;
 // because line of 1/2 with emb 1/4(2,3,3)

-5*t^4/&*[1-t^i : i in [1,1,3,3]];

  // ?? exactly "balanced" normal bundle
  // deg 5/(3*3) = 5 times the unit
  // a = 0, b = -5,
  // E1 = Oh(-4), E2 = Oh(-2), E1-E2 = Oh(-2), deg = -10,
  whereas 6*a-2*b = -2, genus = 6

=========== digress to catch 1/4(2,3,3)
[1,2,3,4,7,17],
d := 17; A := [1,2,3,4,7]; B := [[3,1,1,1],[7,1,2,4]];
D := P(d,A) - PA(A) - Pb(B) - 1/(2*4)*Phalfc() -1/8*Phalfc();
  // -t^4/&*[1-t^i : i in [1,1,2,4]]; 
c4233 := 1/8*Phalfc() -t^4/&*[1-t^i : i in [1,1,2,4]];
   P(d,A) eq PA(A) + Pb(B)  + 1/8*Phalfc() + c4233; // true

[1,3,3,5,6,18],
d := 18; A := [1,3,3,5,6]; B := [[5,1,1,3]];
D := P(d,A) - PA(A) - Pb(B);
  // 3*(t^3 + t^5)/&*[1-t^i : i in [1,1,3,3]];
  // deg = 3/(3*3)
  // a = 3, b = 0
  // E1 = Oh(-1), E2 = Oh(-5), E1-E2 = Oh(4), deg = 12,
  whereas 6*a-2*b = 16, g = 4.
  
[1,3,3,11,18,36]
d := 36; A := [1,3,3,11,18]; B := [[11,1,3,7]];
D := P(d,A) - PA(A) - Pb(B);
  // 2*(2*t^5 + t^4 + 2*t^3)/&*[1-t^i : i in [1,1,3,3]];
  // deg = 36/(3*3*18) = 2/9
  // a = 4, b = 2
  // E1 = Oh(-1), E2 = Oh(-11), E1-E2 = Oh(10), deg = 20,
  whereas 6*a-2*b = 22, g = 5

[1,3,3,14,21,42],
d:=42; A:=[1,3,3,14,21]; B := [[7,1,3,3]];
D := P(d,A) - PA(A) - Pb(B);
  // (5*t^5 + 3*t^4 + 5*t^3)/&*[1-t^i : i in [1,1,3,3]];
  // deg 42/(3*3*21) = 2/9
  // a = 5, b = 3
  // E1 = Oh(-1), E2 = Oh(-14), E1-E2 = Oh(13), deg = 26,
  whereas 6*a-2*b = 28, g = 6.

[1,3,5,6,15,30]
d := 30; A := [1,3,5,6,15]; B := [[5,1,1,3],[5,1,1,3]];
D := P(d,A) - PA(A) - Pb(B);
 // (t^3 + t^5)/&*[1-t^i : i in [1,1,3,3]];
 // deg 30/(3*6*15) = 1/9
  // a = 1, b = 0
  // E1 = Oh(-1), E2 = Oh(-5), E1-E2 = Oh(4), deg = 4,
  whereas 6*a-2*b = 4, g = 2.

[2,3,3,8,16,32],
d := 32; A := [2,3,3,8,16]; B := [];
D := P(d,A) - PA(A) - Pb(B) - 32/(2*8*16)*Phalfc() - 2*c8233;
  // (-6*t^5 - 7*t^4 - 6*t^3)/&*[1-t^i : i in [1,1,3,3]];
  // a = -6, b = -7
  // E1 = Oh(-16), E2 = Oh(-2-8+32) = Oh(22), E1-E2 = Oh(-38), deg = 6*a-2*b
  
  Rule: if the line of 1/3(1,2) is a coordinate line then it has
  deg 1/(3*3) and E1 - E2 = Oh(4*a+2*b)

In the 8 "whereas" cases, don't know how to determine a, b in terms of
C, deg E1, deg E2.