Variation of canonical heights of subvarieties for polarized endomorphisms

• DOI: 10.5802/jtnb.1310
• Publication Date: 2025-03-31T16:41:08Z
• Authors: Thomas Gauthier; Gabriel Vigny
• Keywords: Variation (astronomy)

When an endomorphism f:X→X of a projective variety which is polarized by ample line bundle L, i.e. such that f * L≃L ⊗d with d≥2, defined over number field, Call and Silverman canonical height h ^ for f. In family (𝒳,f,ℒ) parametrized curve S together section P:S→𝒳, they show t (P(t))/h(t) converges to the η (P ) on generic fiber.