Noether inequality for irregular threefolds of general type

Yong Hu; Tong Zhang

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arXiv · 2402.17468

Noether inequality for irregular threefolds of general type

Yong Hu·Tong Zhang

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Abstract

Let $X$ be a smooth irregular $3$-fold of general type over $\mathbb{C}$. We prove that the optimal Noether inequality $$ \mathrm{vol}(X) \ge \frac{4}{3}p_g(X) $$ holds if $p_g(X) \ge 16$ or if $X$ has a Gorenstein minimal model. Moreover, when $X$ attains the equality and $p_g(X) \ge 16$, its canonical model can be explicitly described.

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Yong Hu, Tong Zhang. 2024-02-27. Noether inequality for irregular threefolds of general type. https://arxiv.org/abs/2402.17468

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