On the canonical volume of 3-folds of general type with P₁₂≥ 2

2014/07/30 by Lingzi Hou, Hou, Lingzi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1407.7922

arxiv created 2014/07/30 · arxiv updated 2014/07/31

Abstract

Let V be a nonsingular projective 3-fold of general type. When the pluricanonical section index δ(V)>12, Chen-Chen \citeChen3 has a complete list of the possibility for the weighted basket \mathbb B(V). However the possibility of \mathbb B(V) could be infinite in the situation δ(V)≤ 12, which is the main challenge to the classification. In this paper we mainly study the case with δ(V)=12 and show that Vol(V)≥ (31)/(48048), which improves the corresponding result of Chen--Chen \cite[Prop. 4.9(5)]Chen3.

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