2018/09/14 by Gal Binyamini, Binyamini, Gal · 3 citations
Mathematics · #03C98 #11G18 (primary) #11G50 #14G35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1809.05302
openalex publication_date 2018/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X⊂ Y(1)n be a subvariety defined over a number field \mathbb F and let (P1,…,Pn)∈ X be a special point not contained in a positive-dimensional special subvariety of X. We show that the if a coordinate Pi corresponds to an order not contained in a single exceptional Siegel-Tatuzawa imaginary quadratic field K_* then the associated discriminant |Δ(Pi)| is bounded by an effective constant depending only on deg X and [\mathbb F:\mathbb Q]. We derive analogous effective results for the positive-dimensional maximal special subvarieties. From the main theorem we deduce various effective results of André-Oort type. In particular we define a genericity condition on the leading homogeneous part of a polynomial, and give a fully effective André-Oort statement for hypersurfaces defined by polynomials satisfying this condition.