If C is a g-nodal canonical curve with normalization ν: PP1 →PPg-1 then a line bundle L of degree k on C is given by ν*(OOPP1(k))≅L and gluing data (bj)/(aj):OOPP1⊗kk(Pj)→OOPP1⊗kk(Qj). Given 2g points Pi, Qi and the multipliers (ai,bi) we can compute a basis of sections of L as a kernel of the matrix A=(A)ij with Aij=biBj(Pi)-aiBj(Qi) where Bj:PP1→kk, (p0:p1)→p0k-jp1j.
i1 : (k,g,n)=(4,8,1000); |
i2 : time (P,Q,multL,f)=pickGoodPoints(k,g,n); -- used 0.147619 seconds |
i3 : time f'=lineBundleFromPointsAndMultipliers(multL,P,Q,k); -- used 0.026673 seconds ZZ 1 ZZ 2 o3 : Matrix (----[x , x ]) <--- (----[x , x ]) 1009 0 1 1009 0 1 |
i4 : ideal f==ideal f' o4 = true |