Effective generation for foliated surfaces: results and applications

Abstract

We explore the birational structure and invariants of a foliated surface $(X,\mathcal{F})$ in terms of the adjoint divisor $K_{\mathcal{F}}+\epsilon K_X$, $0<\epsilon \ll 1$. 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 $\epsilon$-adjoint canonical models of foliations of general type and with fixed volume form a bounded family.

arXiv commentv2: 43 pages. Expanded and improved the exposition. Main results are unchanged; v1: 32 pages. Comments are welcome!

References in corpus (7)

• Higher dimensional foliated Mori theory
• Codimension one foliations with numerically trivial canonical class on singular spaces
• Effective algebraic integration in bounded genus
• MMP for co-rank one foliations on threefolds
• Some remarks on the volume of log varieties
• Boundedness of minimal partial du Val resolutions of canonical surface foliations
• On the order of the automorphism group of foliations

Cited by in corpus (3)

• On global ACC for foliated threefolds
• Uniform rational polytopes of foliated threefolds and the global ACC
• Analytic varieties invariant by foliations and Pfaff systems