Explicit birational geometry of 3-folds of general type, I

2008/10/28 by Chen, Jungkai A., Chen, Meng · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0810.5041

Abstract

Let V be a complex nonsingular projective 3-fold of general type. We prove P₁₂(V):=dim H⁰(V, 12K_V)>0 and P_m0(V)>1 for some positive integer m₀≤ 24. A direct consequence is the birationality of the pluricanonical map φ_m for all m≥ 126. Besides, the canonical volume Vol(V) has a universal lower bound ν(3)≥ (1)/(63⋅ 126²).

Cited by

• On minimal 3-folds with K³≥ 86

Related

• Explicit birational geometry of threefolds of general type
• Explicit birational geometry of 3-folds of general type, II
• On the pluricanonical map and the canonical volume of projective 4-folds of general type
• On the pluricanonical map of projective 3-folds of general type with P₃ ≥ 2
• The relative pluricanonical stability for 3-folds of general type