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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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