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4 Ring Maps
 4.1 Ring Maps: Attributes
 4.2 Ring Maps: Operations and Functions

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 \(MultiProj(\textit{R})\) into the projective space according to \(P(W_1)\times P(W_2) \to P(W_1\otimes W_2)\).

4.2-2 PlueckerMap
‣ PlueckerMap( l, n, A, s )( method )

Returns: a homalg ring map

The ring map corresponding to the Pl├╝cker 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 \(\textit{n}+1\).

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 \(P^{\textit{n}}(\textit{A})=P(W)\) 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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