# resonanceDet -- compute the resonance determinant of the crucial constant strand of a degenerate K3 X_e(a,a)

## Synopsis

• Usage:
(d1,d2) = resonanceDet(a)
• Inputs:
• Outputs:
• d1, , the integer factor
• d2, , the resonance factor in ZZ[e_1,e_2]

## Description

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) -- 0.0272893 seconds elapsed -- 0.000029896 seconds elapsed -- 0.000076318 seconds elapsed -- 0.000064467 seconds elapsed -- 0.000122213 seconds elapsed -- 0.000131391 seconds elapsed -- 0.000128895 seconds elapsed -- 0.000036704 seconds elapsed -- 0.000098548 seconds elapsed -- 0.000122903 seconds elapsed -- 0.000135934 seconds elapsed -- 0.000130202 seconds elapsed -- 0.000084973 seconds elapsed -- 0.000106465 seconds elapsed -- 0.000061522 seconds elapsed -- 0.000061272 seconds elapsed -- 0.000020395 seconds elapsed -- 0.000099098 seconds elapsed -- 0.000020134 seconds elapsed (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