2015/08/21 by Padmavathi Srinivasan, Srinivasan, Padmavathi · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1508.05172
arxiv created 2015/08/21 · openalex publication_date 2015/08/21 · arxiv updated 2015/08/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let C be a hyperelliptic curve of genus g over the fraction field K of a discrete valuation ring R. Assume that the residue field k of R is perfect and that \mathop\textrmchar k ≠ 2. Assume that the Weierstrass points of C are K-rational. Let S = \mathop\textrmSpec R. Let X be the minimal proper regular model of C over S. Let \mathop\textrmArt (X/S) denote the Artin conductor of the S-scheme X and let ν(Δ) denote the minimal discriminant of C. We prove that -\mathop\textrmArt (X/S) ≤ ν(Δ). As a corollary, we obtain that the number of components of the special fiber of X is bounded above by ν(Δ)+1.