We compute the minimal resolution F of degenerate K3 Xe(a,a) over ZZ[e1,e2] where deg ei =i and the variables x0,..xa,y0..yb have degrees deg xi=i+1 and deg yi=1. The equations of Xe(a,b) are homogeneous with respect to this grading. Viewed as a resolution over QQ(e1,e2), 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) -- 0.0301763 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 -- 0.000037773 seconds elapsed (e )(-1) 1 0 1 total: 2 2 7: 2 . 8: . 2 -- 0.000167522 seconds elapsed 2 (e ) (e )(-1) 1 2 0 1 total: 2 2 7: 2 . 8: . . 9: . 2 -- 0.000123335 seconds elapsed 2 2 (e ) (e ) 1 2 0 1 total: 3 3 7: 2 . 8: 1 . 9: . 1 10: . 2 -- 0.000150492 seconds elapsed 2 4 (e ) (e ) (-3) 1 2 0 1 total: 4 4 7: 1 . 8: 1 . 9: 2 2 10: . 1 11: . 1 -- 0.00015631 seconds elapsed 2 4 (e ) (e ) (3) 1 2 0 1 total: 4 4 8: 1 . 9: 2 1 10: 1 2 11: . 1 -- 0.0001393 seconds elapsed 2 3 (e ) (e ) (3) 1 2 0 1 total: 1 1 9: 1 1 -- 0.000048112 seconds elapsed (e )(-1) 1 0 1 total: 2 2 9: 1 1 10: 1 1 -- 0.000111938 seconds elapsed 2 (e ) 1 0 1 total: 4 4 9: 2 1 10: 1 1 11: 1 2 -- 0.000132661 seconds elapsed 2 2 (e ) (e ) (-1) 1 2 0 1 total: 4 4 9: 1 . 10: 2 1 11: 1 2 12: . 1 -- 0.000140466 seconds elapsed 2 3 (e ) (e ) (3) 1 2 0 1 total: 4 4 9: 1 . 10: 1 . 11: 2 2 12: . 1 13: . 1 -- 0.000100081 seconds elapsed 2 4 (e ) (e ) (3) 1 2 0 1 total: 4 4 9: 2 1 10: 1 1 11: 1 2 -- 0.000089269 seconds elapsed 2 2 (e ) (e ) (-1) 1 2 0 1 total: 3 3 10: 2 . 11: 1 . 12: . 1 13: . 2 -- 0.000080666 seconds elapsed 2 4 (e ) (e ) (3) 1 2 0 1 total: 2 2 10: 1 1 11: 1 1 -- 0.000070174 seconds elapsed 2 (e ) 1 0 1 total: 2 2 11: 2 . 12: . . 13: . 2 -- 0.000067353 seconds elapsed 2 2 (e ) (e ) 1 2 0 1 total: 1 1 11: 1 1 -- 0.000024859 seconds elapsed (e ) 1 0 1 total: 2 2 12: 2 . 13: . 2 -- 0.000073353 seconds elapsed 2 (e ) (e )(-1) 1 2 0 1 total: 1 1 13: 1 1 -- 0.000026559 seconds elapsed (e ) 1 6 32 32 o2 = (3 , (e ) (e ) ) 1 2 o2 : Sequence |