Addendum to "The Noether inequality for algebraic threefolds"

In this short note, we give a refinement of our previous work (arXiv:1803.05553) stating that for a projective $3$-fold $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 11$, $\text{vol}(X)\geq \frac{4}{3}p_g(X)-{\frac{10}{3}}.$

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