lineBundleFromPointsAndMultipliers -- Computes basis of a line bundle from the 2g points P_i, Q_i and the multipliers

Synopsis

Usage:
lineBundleFromPointsAndMultipliers(multL,P,Q,k)
Inputs:
- multL, a list, containing the normalized multipliers a_i (normalized means that b_i=1)
- P, a matrix, coordinate matrix of g points in P¹
- Q, a matrix, coordinate matrix of g points in P¹
- k, an integer, defining the degree of the line bundle
Outputs:
- f, a matrix, a basis of sections of the line bundle defined by the points P_i, Q_i and the multipliers

Description

If C is a g-nodal canonical curve with normalization ν: P¹ →P^g-1 then a line bundle L of degree k on C is given by ν^*(O_P¹(k))≅L and gluing data (b_j)/(a_j):O_P¹⊗kk(P_j)→O_P¹⊗kk(Q_j). Given 2g points P_i, Q_i and the multipliers (a_i,b_i) we can compute a basis of sections of L as a kernel of the matrix A=(A)_ij with A_ij=b_iB_j(P_i)-a_iB_j(Q_i) where B_j:P¹→kk, (p₀:p₁)→p₀^k-jp₁^j.

Ways to use `lineBundleFromPointsAndMultipliers` :

lineBundleFromPointsAndMultipliers(List,Matrix,Matrix,ZZ)

lineBundleFromPointsAndMultipliers -- Computes basis of a line bundle from the 2g points P_i, Q_i and the multipliers

Synopsis

Description

See also

Ways to use lineBundleFromPointsAndMultipliers :

Ways to use `lineBundleFromPointsAndMultipliers` :