Lower bounds for zero-dimensional projections

Authors:
W. Dale Brownawell;Chee K. Yap
Affiliations:
Penn State University, University Park, PA, USA;Courant Institute, New York University, New York, NY, USA
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

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Abstract

Let I be an ideal generated by polynomials P1, ...Pm, ∈ Z[X1,...,Xn], and β be an isolated prime component of I. If the projection of ZERO(β)⊆Cn onto the first coordinate is a finite set, and ¶=(¶1,...,¶n) ∈ZERO(β) where ¶1 0, then we prove a lower bound on |¶| in terms of n, m and the maximum degree D and maximum height H of the polynomials.