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arXiv · 1407.7922

On the canonical volume of 3-folds of general type with $P_{12}\geq 2$

Lingzi Hou
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Abstract

Let $V$ be a nonsingular projective 3-fold of general type. When the pluricanonical section index $δ(V)>12$, Chen-Chen \cite{Chen3} 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 $δ(V)\leq 12$, which is the main challenge to the classification. In this paper we mainly study the case with $δ(V)=12$ and show that $Vol(V)\geq \frac{31}{48048}$, which improves the corresponding result of Chen--Chen \cite[Prop. 4.9(5)]{Chen3}.

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Lingzi Hou. 2014-07-30. On the canonical volume of 3-folds of general type with $P_{12}\geq 2$. https://arxiv.org/abs/1407.7922

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