GAP (GradedModules) - Chapter 4: Ring Maps

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4 Ring Maps
4.1 Ring Maps: Attributes
4.1-1 KernelSubobject
4.2 Ring Maps: Operations and Functions
4.2-1 SegreMap
4.2-2 PlueckerMap
4.2-3 VeroneseMap

### 4 Ring Maps

#### 4.1 Ring Maps: Attributes

##### 4.1-1 KernelSubobject

`‣ KernelSubobject`( phi ) | ( method )

Returns: a homalg submodule

The kernel ideal of the ring map phi.

#### 4.2 Ring Maps: Operations and Functions

##### 4.2-1 SegreMap

`‣ SegreMap`( R, s ) | ( method )

Returns: a homalg ring map

The ring map corresponding to the Segre embedding of MultiProj(R) into the projective space according to P(W_1)× P(W_2) -> P(W_1⊗ W_2).

##### 4.2-2 PlueckerMap

`‣ PlueckerMap`( l, n, A, s ) | ( method )

Returns: a homalg ring map

The ring map corresponding to the Plücker embedding of the Grassmannian G_l(P^n(A))=G_l(P(W)) into the projective space P(⋀^l W), where W=V^* is the A-dual of the free module V=A^n+1 of rank n+1.

##### 4.2-3 VeroneseMap

`‣ VeroneseMap`( n, d, A, s ) | ( method )

Returns: a homalg ring map

The ring map corresponding to the Veronese embedding of the projective space P^n(A)=P(W) into the projective space P(S^d W), where W=V^* is the A-dual of the free module V=A^n+1 of rank n+1.

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