Effective generation for foliated surfaces: results and applications

2021/04/23 by Calum Spicer, Spicer, Calum, Roberto Svaldi +1 · 4 citations
Mathematics · #14E30 #32S65 #37F75 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.2104.11540

openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore the birational structure and invariants of a foliated surface (X, \mathcal F) in terms of the adjoint divisor K_{\mathcal F}+εK_X, 0< ε≪ 1. We then establish a bound on the automorphism group of an adjoint general type foliated surface (X, \mathcal F), provide a bound on the degree of a general curve invariant by an algebraically integrable foliation on a surface and prove that the set of ε-adjoint canonical models of foliations of general type and with fixed volume form a bounded family.

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Adjoint log canonical foliated singularities on surfaces
• Explicit bounds on foliated surfaces and the Poincaré problem
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures

Related

• Canonical Models of Adjoint Foliated Structures on Surfaces
• Explicit bounds on foliated surfaces and the Poincaré problem
• On birational boundedness of foliated surfaces
• Boundedness of polarized foliated surfaces
• Adjoint log canonical foliated singularities on surfaces