Title of article :
Implicitization of rational surfaces using toric varieties
Author/Authors :
Amit Khetan، نويسنده , , Carlos DʹAndrea، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
Pages :
23
From page :
543
To page :
565
Abstract :
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit equation of such a rational parameterized surface. The first approach uses resultant matrices and gives an exact determinantal formula for the implicit equation if the parameterization has no base points. In the case the base points are isolated local complete intersections, we show that the implicit equation can still be recovered by computing any non-zero maximal minor of this matrix. The second method is the toric extension of the method of moving surfaces, and involves finding linear and quadratic relations (syzygies) among the input polynomials. When there are no base points, we show that these can be put together into a square matrix whose determinant is the implicit equation. Its extension to the case where there are base points is also explored.
Keywords :
Toric varieties , syzygies , implicitization , Resultants
Journal title :
Journal of Algebra
Serial Year :
2006
Journal title :
Journal of Algebra
Record number :
697660
Link To Document :
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