2007/03/03 by Donghoon Hyeon, Hyeon, Donghoon, Yongnam Lee +1 · 3 citations
Computer Science · Mathematics · #14E30 #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Polynomial and algebraic computation #math.AG #msc:14E30 #msc:14H10
paper · pdf · doi:10.48550/arxiv.math/0703093
35 pages, 6 figures
arxiv created 2007/03/03 · openalex publication_date 2007/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we completely work out the log minimal model program for the moduli space of stable curves of genus three. We employ a rational multiple αδ of the divisor δ of singular curves as the boundary divisor, construct the log canonical model for the pair (\mathcal M3, αδ) using geometric invariant theory as we vary α from one to zero, and give a modular interpretation of each log canonical model and the birational maps between them. By using the modular description, we are able to identify all but one log canonical models with existing compactifications of M3, some new and others classical, while the exception gives a new modular compactification of M3.