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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 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 $$\textit{n}+1$$.

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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