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

Abstract

<p style='text-indent:20px;'>We show that, for any nonsingular projective 4-fold <inline-formula><tex-math id="M2">\begin{document}$ V $\end{document}</tex-math></inline-formula> of general type with geometric genus <inline-formula><tex-math id="M3">\begin{document}$ p_g\geq 2 $\end{document}</tex-math></inline-formula>, the pluricanonical map <inline-formula><tex-math id="M4">\begin{document}$ \varphi_{33} $\end{document}</tex-math></inline-formula> is birational onto the image and the canonical volume <inline-formula><tex-math id="M5">\begin{document}$ {\rm Vol}(V) $\end{document}</tex-math></inline-formula> has the lower bound <inline-formula><tex-math id="M6">\begin{document}$ \frac{1}{480} $\end{document}</tex-math></inline-formula>, which improves a previous theorem by Chen and Chen.</p>