A sharp lower bound for the canonical volume of 3-folds of general type

2004/07/23 by Meng Chen, Chen, Meng
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0407397

Final version, 22 pages, to appear in Math. Annalen

openalex publication_date 2004/07/23 · arxiv created 2005/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a smooth projective 3-fold of general type. Denote by K³, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K³ as the canonical volume of V. Assume p_g≥ 2. We show that K³≥ 1/3, which is a sharp lower bound. Then we classify those V with small K³ up to explicit tructure. We also give some new examples with p_g=2 which have maximal canonical stability index. Finally we give an application to certain algebraic 4-folds.

Citations

• Pluricanonical systems of projective 3-folds of general type

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