Equations for the projective closure and effective Nullstellensatz

Abstract Let k be a field and V be an algebraic subset of the affine space A(kn) given by a family of polynomials with degrees bounded. The projective closure pcl(V) of V in Pn is the smallest closed projective subset of Pn containing V. We describe an efficiently parallelisable subexponential time algorithm to compute equations for pcl(V). We also show how equations for pcl(V) can be obtained by suitably truncated Groebner basis algorithms. The proof of the two algorithms are based on an effective Nullstellensatz.

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