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We describe a new method of constructing rational surfaces with given invariants in P 4 and present a family of degree 11 rational surfaces of sectional genus 11 with 2 six-secants that we found with this method.

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and Bézier triangles, we identify a… (More)

We provide some statistics about an irreducibil-ity/reducibility test for multivariate polynomials over finite fields based on counting points. The test works best for polynomials in a large number of variables and can also be applied to black box polynomials.

We prove that the moduli space C(d) of plane curves of degree d (for projective equivalence) is rational except possibly if

We show how to use experiments over finite fields to gain information about the solution set of polynomial equations in characteristic zero.

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