Revision 024c9750ac3f39428818576cba043d57e6a7f2c1 authored by Mohamed Barakat on 09 July 2015, 13:37:30 UTC, committed by Mohamed Barakat on 09 July 2015, 16:29:51 UTC
1 parent cea8169
example1.g
LoadPackage( "ToricVarieties" );
## We start with affine varieties, 3 and 2 dimensional.
sigma1 := Cone( [ [1,0,0], [0,1,0], [1,0,1], [0,1,1] ] );
U1 := ToricVariety( sigma1 );
## We first check the properties
Dimension( U1 );
IsSmooth( U1 );
IsOrbifold( U1 );
IsAffine( U1 );
IsProjective( U1 );
HasTorusfactor( U1 );
DimensionOfTorusfactor( U1 );
## We already know this variety
CoordinateRing( U1, "x" );
## and for further computations, we might set
CoordinateRingOfTorus( U1, [ "x", "y", "z" ] );
## Maybe we ask about the divisorgroup.
TorusInvariantDivisorGroup( U1 );
## And the class group
ClassGroup( U1 );
## This resultant now is something we know
PicardGroup( U1 );
## as this holds
IsAffine( U1 );
#####
##### We want to have a look at the divisors.
#####
P := TorusInvariantPrimeDivisors( U1 );
List( P, IsPrincipal );
## This suprises, we take a look
List( P, ClassOfDivisor );
## And might get lucky with this one
D := P[ 1 ] + P[ 2 ];
## This one seems to be better
IsPrincipal( D );
## and
IsCartier( D );
## Maybe we take a last look at the sheaf
BasisOfGlobalSectionsOfDivisorSheaf( D );
## We already know that we wont get any ample divisors
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