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Projective.gi
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Projective.gi
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# SPDX-License-Identifier: GPL-2.0-or-later
# ZariskiFrames: (Co)frames/Locales of Zariski closed/open subsets of affine, projective, or toric varieties
#
# Implementations
#
##
InstallMethod( ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety ],
function( A )
local L, S, B;
L := ListOfMorphismsOfRank1RangeOfUnderlyingCategory( A );
L := List( L, UnderlyingMatrix );
S := UnderlyingRing( A );
B := IrrelevantIdealColumnMatrix( S );
B := List( [ 1 .. NrRows( B ) ], r -> CertainRows( B, [ r ] ) );
L := List( L, mat -> List( B, r -> Saturate( mat, r ) ) );
L := Concatenation( L );
L := List( L, AsMorphismInCategoryOfRows );
A!.ListOfMorphismsOfRank1RangeOfUnderlyingCategory := L;
return L;
end );
##
InstallMethod( ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety and HasListOfReducedMorphismsOfUnderlyingCategory ],
ListOfReducedMorphismsOfUnderlyingCategory );
##
InstallMethod( ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety and HasReducedMorphismOfUnderlyingCategory ],
ListOfReducedMorphismsOfUnderlyingCategory );
##
InstallMethod( ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety and HasStandardMorphismOfUnderlyingCategory ],
function( A )
return [ StandardMorphismOfUnderlyingCategory( A ) ];
end );
##
InstallMethod( SaturatedMorphismOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety ],
function( A )
A := ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory( A );
return ITERATED_INTERSECTION_OF_IDEALS_USING_CategoryOfRows( A );
end );
##
InstallMethod( SaturatedMorphismOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety and HasReducedMorphismOfUnderlyingCategory ],
ReducedMorphismOfUnderlyingCategory );
##
InstallMethod( SaturatedMorphismOfRank1RangeOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety and HasStandardMorphismOfUnderlyingCategory ],
StandardMorphismOfUnderlyingCategory );
##
InstallMethod( ListOfReducedMorphismsOfUnderlyingCategory,
"for an object in a Zariski frame or coframe of a projective variety",
[ IsObjectInZariskiFrameOrCoframeOfAProjectiveVariety ],
function( A )
local L, S, B;
L := ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory( A );
L := List( L, UnderlyingMatrix );
L := List( L, UnderlyingMatrixOverNonGradedRing );
L := List( L, RadicalSubobjectOp );
S := UnderlyingRing( A );
L := List( L, mat -> S * mat );
L := List( L, AsMorphismInCategoryOfRows );
A!.ListOfSaturatedMorphismsOfRank1RangeOfUnderlyingCategory := L;
return L;
end );