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The sharp lower bound for the volume of threefolds of general type with \({\chi({\mathcal O}_X)=1}\)

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Abstract

Let V be a smooth projective threefold of general type. Denote by K 3, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K 3 as a canonical volume of V. The paper is devoted to proving the sharp lower bound \({K^{3} \ge \frac{1}{420}}\) which can be reached by an example: \({X_{46} \subseteq \mathbb{P}(4,5,6,7,23)}\).

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Lei Zhu

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  1. Lei Zhu
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Correspondence to Lei Zhu.

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Lei Zhu was supported by Fudan Graduate Students’ Innovation Projects (EYH5928004).

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Zhu, L. The sharp lower bound for the volume of threefolds of general type with \({\chi({\mathcal O}_X)=1}\) . Math. Z. 261, 123–141 (2009). https://doi.org/10.1007/s00209-008-0316-7

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  • DOI: https://doi.org/10.1007/s00209-008-0316-7

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