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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08089 |
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Table of Contents:
- Let $D$ be a big integral divisor on a smooth projective surface $X$. In this paper, we study Noether-type inequalities for $D$. The key ingredient is the introduction of a numerical invariant $\mathfrak{e}(D)$, which depends only on the negative part $N$ of $D$. In particular, $\mathfrak{e}(D)=0$ if $D$ is nef. As an application, we establish an inequality between the volume and the pluri-sectional index of a canonical foliated surface of general type.