Ideals of numerically generic realizations of configurations of Lines
نویسندگان
چکیده
Generic realizations of configurations of lines as reducible projective varieties in Pn are constructed numerically. Examples are taken from projections of abstract seminormal configurations and the classical geometry related to Schläfli’s double-six configuration. The ideal defining the homogeneous coordinate ring of a realization is calculated along with its Hilbert Function, identifying which examples are complete intersections. In particular a generic Schläfli double-six is constructed and shown to be the complete intersection of a cubic and quartic surface. Using the numerical algebraic geometry software Bertini, it is then possible to give explicit equations for all 27 lines on this cubic surface.
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تاریخ انتشار 2008