Weak boundedness theorems for canonically fibered Gorenstein minimal threefolds

2002/06/10 by Meng Chen, Chen, Meng
Mathematics · #14C20 #14E35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14C20 #msc:14E35

paper · pdf · doi:10.48550/arxiv.math/0206097

AMS-Latex, 9 pages, Proc. AMS (to appear)

openalex publication_date 2002/06/10 · arxiv created 2004/01/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by F a smooth model of a generic irreducible component in fibers of the canonical map of X and so F is a smooth curve or a smooth surface. The main result of the paper is that there is a computable constant K (independent of X) such that g(F)≤ 647 or p_g(F)≤ 38 whenever p_g(X)≥ K. The method heavily relies on both a Noether type of inequality and a Miyaoka-Yau inequality and that is the reason we only treat a Gorenstein object here. It is open whether the degree of the canonical map is universally bounded when the canonical map is generically finite.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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