2018/12/13 by María Isabel Herrero, Herrero, Maria Isabel, Gabriela Jeronimo +3
Computer Science · Mathematics · #13P99 #14Q20 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1812.05505
openalex publication_date 2018/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove new upper bounds for the degrees in Hilbert's Nullstellensatz and for the Noether exponent of polynomial ideals in terms of the monomial structure of the polynomials involved. Our bounds improve the previously known bounds in the sparse setting and are the first to take into account the different supports of the polynomials.