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arXiv · 2410.08465

The canonical map of a foliated surface of general type

Xin Lü
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Abstract

Let $(S,\mathcal{F})$ be a foliated surface over the complex number of general type, i.e., the Kodaira dimension $\mathrm{Kod}(\mathcal{F})=2$. We study the geometry of the canonical map $\varphi$ of the foliated surface $(S,\mathcal{F})$, and prove several boundedness results on the canonical map $\varphi$, generalizing Beauville's beautiful work on the canonical maps of algebraic surfaces to foliated surfaces. As an application, we prove three Noether type inequalities for $(S,\mathcal{F})$ depending on the Kodaira dimension of the surface $S$.

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Xin Lü. 2024-10-11. The canonical map of a foliated surface of general type. https://arxiv.org/abs/2410.08465

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