GAP (GradedModules) - Chapter 2: Ring Maps

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2 Ring Maps
2.1 Ring Maps: Attributes
2.1-1 KernelSubobject
2.2 Ring Maps: Operations and Functions
2.2-1 SegreMap
2.2-2 PlueckerMap
2.2-3 VeroneseMap

### 2 Ring Maps

#### 2.1 Ring Maps: Attributes

##### 2.1-1 KernelSubobject

`‣ KernelSubobject`( phi ) | ( method )

Returns: a homalg submodule

The kernel ideal of the ring map phi.

#### 2.2 Ring Maps: Operations and Functions

##### 2.2-1 SegreMap

`‣ SegreMap`( R, s ) | ( method )

Returns: a homalg ring map

The ring map corresponding to the Segre embedding of \(MultiProj(\textit{R})\) into the projective space according to \(P(W_1)\times P(W_2) \to P(W_1\otimes W_2)\).

##### 2.2-2 PlueckerMap

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

Returns: a homalg ring map

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

##### 2.2-3 VeroneseMap

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

Returns: a homalg ring map

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

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