Explicit birational geometry of threefolds of general type

2007/06/20 by Jungkai A. Chen, Chen, Jungkai A., Chen, Meng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0706.2987

openalex publication_date 2007/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a complex nonsingular projective 3-fold of general type. We prove P₁₂(V)>0 and P₂₄(V)>1 (which answers an open problem of J. Kollar and S. Mori). We also prove that the canonical volume has an universal lower bound Vol(V) ≥ 1/2660 and that the pluri-canonical map Φ_m is birational onto its image for all m≥ 77. As an application of our method, we prove Fletcher's conjecture on weighted hyper-surface 3-folds with terminal quotient singularities. Another featured result is the optimal lower bound Vol(V)≥ 1/420 among all those 3-folds V with χ(\mathcal O_V)≤ 1.

Related

• Explicit birational geometry of 3-folds of general type, I
• Explicit birational geometry of 3-folds of general type, II
• Explicit birational geometry of 3-folds, Foreword
• Projective 3-folds of general type with X=1
• Complex projective threefolds with non-negative canonical Euler-Poincare characteristic