### Abstract

Let I be an ideal generated by polynomials P_{1}, . . . , P _{m} ∈ ℤ[X_{1}, . . . , X_{n}], and β be an isolated prime component of I. If the projection of Zero(β) ⊆ ℂ^{n} onto the first coordinate is a finite set, and ζ = (ζ_{1}, . . . , ζ_{n}) ∈ Zero(β) where ζ_{1} ≠ 0, then we prove a lower bound on |ζ_{1}| in terms of n,m and the maximum degree D and maximum height H of the polynomials.

Original language | English (US) |
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Title of host publication | ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation |

Pages | 79-85 |

Number of pages | 7 |

DOIs | |

State | Published - 2009 |

Event | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of Duration: Jul 28 2009 → Jul 31 2009 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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### Other

Other | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 7/28/09 → 7/31/09 |

### Keywords

- Chow forms
- Exact geometric computation
- Exact numerical algorithms
- Nullstellensatz
- Transcendence theory
- Zero bounds

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Brownawell, W. D., & Yap, C. K. (2009). Lower bounds for zero-dimensional projections. In

*ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation*(pp. 79-85). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1576702.1576716