References & Citations
Mathematics > Algebraic Geometry
Title: The Noether inequalities for a foliated surface of general type
(Submitted on 25 Apr 2024)
Abstract: Let $(\mathcal{F},S)$ be a foliated surface of general type with reduced singularities over the complex number. We establish the Noether type inequalities for $(\mathcal{F},S)$. Namely, we prove that $\mathrm{vol}(\mathcal{F}) \geq p_g(\mathcal{F})-2$, and that $\mathrm{vol}(\mathcal{F}) \geq 2p_g(\mathcal{F})-4$ if moreover the surface $S$ is also of general type. Examples show that both of the Noether type inequalities are sharp.
Link back to: arXiv, form interface, contact.