H0(C,KC) ⊕H0(C,KC2⊗L) ⊕H0(C,KC3⊗L2) ⊕...
an artinian reduction by sg-3,sg-2 has shapeA=H0(C,KC) ⊕H0(C,KC2 ⊗L) / H0(C,KC)<sg-3,sg-2> ⊕...
and Hilbert function (g,g-3,1) The desired Koszul matrix is koszul(m,<s0,...,sg-4>) ⊗sB with values in A2 which is returned. The result is a binomial(g-3,m-1) x g*binomial(g-3,m) matrix of binary forms of degree 4g-4 with values in a g-3 dimensional complementary subspace ofH0(C,KC)<sg-3,sg-2> ⊂H0(C,KC2 ⊗L) ⊂kk[x0,x1]4g-4
i1 : (g,n)=(8,2); |
i2 : M=criticalKoszulMatrixForPrymCurve(g,n); ZZ 10 ZZ 40 o2 : Matrix (-----[x , x ]) <--- (-----[x , x ]) 12451 0 1 12451 0 1 |
i3 : isHomogeneous M o3 = true |
i4 : betti syz( M,DegreeLimit=>4*g-4) 0 1 o4 = total: 40 1 27: . 1 28: 40 . o4 : BettiTally |
i5 : m= lift(g/2,ZZ) o5 = 4 |
i6 : (rank target M, rank source M) == (binomial(g-3, m-1), g*binomial(g-3,m)) o6 = true |
i7 : rank source mingens ideal M == g-3 o7 = true |