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7 Relative affine varieties
7.1 Attributes
7.1-1 GraphOfRingMorphism
‣ GraphOfRingMorphism( phi ) | ( attribute ) |
Returns: an object in a Zariski coframe of an affine variety
Compute the graph the morphism of the morphism phi of affine rings.
7.1-2 FunctorClosureOfProjectionBetweenZariskiCoframes
‣ FunctorClosureOfProjectionBetweenZariskiCoframes( arg ) | ( attribute ) |
7.1-3 ClosureOfProjection
‣ ClosureOfProjection( arg ) | ( attribute ) |
7.1-4 ClosureOfImage
‣ ClosureOfImage( phi ) | ( attribute ) |
Returns: a constructible object as a union of formal multiple differences
Compute the image closure of the morphism defined by the morphism phi of affine rings.
7.1-5 FunctorPreimageOfProjectionBetweenZariskiCoframes
‣ FunctorPreimageOfProjectionBetweenZariskiCoframes( arg ) | ( attribute ) |
7.2 Operations
7.2-1 PreimageOfProjection
‣ PreimageOfProjection( arg1, arg2 ) | ( operation ) |
7.2-2 PreimageOfProjection
‣ PreimageOfProjection( arg1, arg2 ) | ( operation ) |
7.2-3 FiberOfProjectionOverBasePoint
‣ FiberOfProjectionOverBasePoint( arg1, arg2 ) | ( operation ) |
7.2-4 FiberOfProjectionOverBasePoint
‣ FiberOfProjectionOverBasePoint( arg1, arg2 ) | ( operation ) |
7.2-5 TangentSpaceOfFiberAtPoint
‣ TangentSpaceOfFiberAtPoint( V, p_base, p_fiber ) | ( operation ) |
Returns: an object in a Zariski coframe of an affine variety
Compute the tangent space of the fiber of V over closed base point p_base at the closed point p_fiber as an affine subspace of the ambient space of V intersecting (p_base, p_fiber).
7.2-6 TangentSpaceOfFiberAtPoint
‣ TangentSpaceOfFiberAtPoint( V, p_base, p_fiber ) | ( operation ) |
7.2-7 DimensionsOfFibrationAtClosedPoint
‣ DimensionsOfFibrationAtClosedPoint( V, p_base, p_fiber ) | ( operation ) |
Returns: a list
7.2-8 DimensionsOfFibrationAtClosedPoint
‣ DimensionsOfFibrationAtClosedPoint( V, p_base, p_fiber ) | ( operation ) |
7.2-9 EmbeddedComplementOfTangentSpaceOfFiberAtPoint
‣ EmbeddedComplementOfTangentSpaceOfFiberAtPoint( V, p_base, p_fiber ) | ( operation ) |
Returns: an object in a Zariski coframe
Compute a compolement of the tangent space of the fiber of V over the closed base point p_base at the closed point p_fiber as an affine subspace of the ambient space of V intersecting (p_base, p_fiber).
7.2-10 EmbeddedComplementOfTangentSpaceOfFiberAtPoint
‣ EmbeddedComplementOfTangentSpaceOfFiberAtPoint( V, p_base, p_fiber ) | ( operation ) |
7.2-11 ClosedSubsetWithGenericallyZeroDimensionalFibers
‣ ClosedSubsetWithGenericallyZeroDimensionalFibers( V, p_base, p_fiber ) | ( operation ) |
Returns: an object in a Zariski coframe of an affine variety
7.2-12 ClosedSubsetOfBaseWithFreeFibersOverComplementOrEmpty
‣ ClosedSubsetOfBaseWithFreeFibersOverComplementOrEmpty( arg ) | ( attribute ) |
7.2-13 ClosedSubsetOfBaseWithFreeFibersOverComplement
‣ ClosedSubsetOfBaseWithFreeFibersOverComplement( arg ) | ( attribute ) |