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D.5.4.7 globalSections

Procedure from library divisors.lib (see divisors_lib).

Usage:
globalSections(A); A = divisor.

Assume:
A is a divisor on X.

Return:
a list with a basis of the space of global sections of D.

Theory:
We assume that the qring of X satisfies the S2-condition and that X is smooth. We compute sat((f*J) : I) /f where D = (I)-(J).

Example:
 
LIB "divisors.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
ring r=31991,(x,y,z),dp;
ideal I = y^2*z - x*(x-z)*(x+3*z);
qring Q = std(I);
divisor P = makeDivisor(ideal(x,z),ideal(1));
divisor D = multdivisor(4,P);
globalSections(D);
==> [1]:
==>    _[1]=x2
==>    _[2]=z2
==>    _[3]=yz
==>    _[4]=xz
==> [2]:
==>    z2