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Speaker: Amit Khetan,
University of Massachusetts, Amherst
Title:
Implicitization of Rational Surfaces using Toric Varieties
Abstract:
The implicitization problem involves finding the defining equations of
a rational variety given by a parameterization. Of particular interest
in Computer Aided Graphic Design and elsewhere is the case of a
surface in three space. In joint work with Carlos D'Andrea we recast
the parameterization in terms of projection from a toric variety.
This allows us to extend two classical implicitization techniques from
homogeneous and bihomogeneous systems to the general toric case. The
first method uses resultant matrices while the second involves
syzygies. Using our techniques we can compute the implicit equation,
without an extraneous factor, in many new situation where previous
methods cannot.
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