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Abstract: Given a parametrization of a rational surface in P^3, it is
sometimes possible to express the equation of the surface as a determinant
whose rows correspond to what are called "moving planes" and "moving
quadrics". Moving plane can be thought of as syzygies among the polynomials
determining the parametrization, and syzygies among the second symmetric
power of these polynomials gives moving quadrics.
Where the parametrization has no base points, everything works fine, but
some of the arguments break down in the presence of base points. This
leads to some interesting questions concerning syzygies among polynomials
with base points.
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schenck@neu.edu