On minimal 4-folds of general type with $ p_g \geq 2 $

Jianshi Yan; Jianshi Yan

doi:10.3934/era.2021040

Electronic Research Archive

2021, Volume 29, Issue 5: 3309-3321. doi: 10.3934/era.2021040

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On minimal 4-folds of general type with $ p_g \geq 2 $

Jianshi Yan

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received: 01 January 2021 Revised: 01 March 2021 Published: 26 May 2021
Primary: 14J35, 14E05; Secondary: 14C20, 14E30

We show that, for any nonsingular projective 4-fold $ V $ of general type with geometric genus $ p_g\geq 2 $, the pluricanonical map $ \varphi_{33} $ is birational onto the image and the canonical volume $ {\rm Vol}(V) $ has the lower bound $ \frac{1}{480} $, which improves a previous theorem by Chen and Chen.
- 4-folds of general type,
- pluricanonical map,
- canonical volume,
- linear system,
- birational geometry
Citation: Jianshi Yan. On minimal 4-folds of general type with $ p_g \geq 2 $[J]. Electronic Research Archive, 2021, 29(5): 3309-3321. doi: 10.3934/era.2021040

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Abstract

We show that, for any nonsingular projective 4-fold $ V $ of general type with geometric genus $ p_g\geq 2 $, the pluricanonical map $ \varphi_{33} $ is birational onto the image and the canonical volume $ {\rm Vol}(V) $ has the lower bound $ \frac{1}{480} $, which improves a previous theorem by Chen and Chen.

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