‣ IsZariskiCoframeOfAProjectiveVariety( object ) | ( filter ) |
Returns: true or false
The GAP category of Zariski coframes of a projective variety.
‣ IsObjectInZariskiCoframeOfAProjectiveVariety( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a Zariski coframe of a projective variety.
‣ IsMorphismInZariskiCoframeOfAProjectiveVariety( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a Zariski coframe of a projective variety.
‣ UnderlyingClosedSubsetOfSpec( arg ) | ( attribute ) |
‣ ZariskiCoframeOfProj( R ) | ( attribute ) |
Returns: a CAP category
Construct the Zariski coframe of closed sets in a projective variety defined as the vanishing loci of (radical) ideals of a homalg ring R.
‣ ClosedSubsetOfProj( mat ) | ( operation ) |
‣ ClosedSubsetOfProj( str, R ) | ( operation ) |
‣ ClosedSubsetOfProjByListOfColumns( L ) | ( operation ) |
Returns: a CAP object
Construct a Zariski closed subset (as an object in the Zariski coframe of closed subsets a projective variety) from the homogeneous matrix mat. The result is the projective support of the module-theoretic cokernel \(M\) of the matrix mat viewed as a morphism in the Freyd category of the associated category of graded rows, i.e., the result is the projective vanishing locus of the (homogeneous) annihilator of \(M\).
‣ ClosedSubsetOfProjByRadicalColumn( I ) | ( operation ) |
‣ ClosedSubsetOfProjByRadicalColumn( str, R ) | ( operation ) |
ClosedSubsetOfProjByRadicalColumn assumes that the image is a radical ideal.
‣ ClosedSubsetOfProjByStandardColumn( I ) | ( operation ) |
‣ ClosedSubsetOfProjByStandardColumn( str, R ) | ( operation ) |
ClosedSubsetOfProjByStandardColumn assumes that the image is a radical ideal given by some sort of a standard
basis.
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