We compute the minimal resolution F of degenerate K3 X_e(a,a) over ZZ[e_1,e_2] where deg e_i =i and the variables x_0,..x_a,y_0..y_b have degrees deg x_i=i+1 and deg y_i=1. The equations of X_e(a,b) are homogeneous with respect to this grading. Viewed as a resolution over QQ(e_1,e_2), this resolution is non-minimal and carries further gradings. We decompose the crucial map of the a-th strand into blocks, compute their determinants, and factor the product.
i1 : a=4 o1 = 4 |
i2 : (d1,d2)=resonanceDet(a)
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(number of blocks= , 18)
(size of the matrices, Tally{1 => 4})
2 => 6
3 => 2
4 => 6
0 1
total: 1 1
7: 1 1
(e )(-1)
1
0 1
total: 2 2
7: 2 .
8: . 2
2
(e ) (e )(-1)
1 2
0 1
total: 2 2
7: 2 .
8: . .
9: . 2
2 2
(e ) (e )
1 2
0 1
total: 3 3
7: 2 .
8: 1 .
9: . 1
10: . 2
2 4
(e ) (e ) (-3)
1 2
0 1
total: 4 4
7: 1 .
8: 1 .
9: 2 2
10: . 1
11: . 1
2 4
(e ) (e ) (3)
1 2
0 1
total: 4 4
8: 1 .
9: 2 1
10: 1 2
11: . 1
2 3
(e ) (e ) (3)
1 2
0 1
total: 1 1
9: 1 1
(e )(-1)
1
0 1
total: 2 2
9: 1 1
10: 1 1
2
(e )
1
0 1
total: 4 4
9: 2 1
10: 1 1
11: 1 2
2 2
(e ) (e ) (-1)
1 2
0 1
total: 4 4
9: 1 .
10: 2 1
11: 1 2
12: . 1
2 3
(e ) (e ) (3)
1 2
0 1
total: 4 4
9: 1 .
10: 1 .
11: 2 2
12: . 1
13: . 1
2 4
(e ) (e ) (3)
1 2
0 1
total: 4 4
9: 2 1
10: 1 1
11: 1 2
2 2
(e ) (e ) (-1)
1 2
0 1
total: 3 3
10: 2 .
11: 1 .
12: . 1
13: . 2
2 4
(e ) (e ) (3)
1 2
0 1
total: 2 2
10: 1 1
11: 1 1
2
(e )
1
0 1
total: 2 2
11: 2 .
12: . .
13: . 2
2 2
(e ) (e )
1 2
0 1
total: 1 1
11: 1 1
(e )
1
0 1
total: 2 2
12: 2 .
13: . 2
2
(e ) (e )(-1)
1 2
0 1
total: 1 1
13: 1 1
(e )
1
6 32 32
o2 = (3 , (e ) (e ) )
1 2
o2 : Sequence
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The object resonanceDet is a method function.