Algebraic stability and degree growth of monomial maps and polynomial maps

2010/07/01 by Jan-Li Lin, Lin, Jan-Li
Mathematics · #37F10 (Primary) 14M25 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1007.0253

openalex publication_date 2010/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a rational monomial map, we consider the question of finding a toric variety on which it is algebraically stable. We give conditions for when such variety does or does not exist. We also obtain several precise estimates of the degree sequences of monomial maps on ¶ⁿ. Finally, we characterize polynomial maps which are algebraically stable on (¶¹)ⁿ.

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