L = lineSchemeFourDim B
This method computes the scheme that parametrizes the set of line modules over an AS-regular algebra B due to Shelton and Vancliff. More precisely, it computes the image of this scheme under the Plücker embedding.
As a first example, we see that the line scheme of the commutative polynomial ring is just the image of the Grassmannian Gr(4,2) in $\mathbb{P}^5$:
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Next, we compute the line scheme of a (-1)-skew polynomial ring. We see that it is a union of four planes and three quadric surfaces.
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Finally, we consider the following AS-regular algebra of dimension four. Its line scheme is dimension one and degree 20, and is a union of 10 conics.
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The object lineSchemeFourDim is a method function.