Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies

ABSTRACT

We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d)for a given integer d ≥1 can be represented and computed from the linear syzygies of its parametrization if the base points are isolated and form locally a complete intersection.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

General Terms:
Algorithms, Theory

Keywords:
approximation complexes, implicitization, linear syzygies