2023/07/20 by Thomas Gauthier, Gauthier, Thomas, Gabriel Vigny +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2307.11243
openalex publication_date 2023/07/20 · openalex created_date 2023/07/25 · openalex updated_date 2026/07/28
When an endomorphism f:X→ X of a projective variety which is polarized by an ample line bundle L, i.e. such that f^*L≃ L⊗ d with d≥2, is defined over a number field, Call and Silverman defined a canonical height \widehathf for f. In a family (X,f,L) parametrized by a curve S together with a section P:S→ X, they show that \widehathft(P(t))/h(t) converges to the height \widehathfη(Pη) on the generic fiber. In the present paper, we prove the equivalent statement when studying the variation of canonical heights of subvarieties Yt varying in a family Y of any relative dimension.