Numerical conditions for the boundedness of foliated surfaces

2024/12/08 by Alessandro Passantino, Passantino, Alessandro · 3 citations
Engineering · #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2412.05986

Abstract

We show that the set of Hilbert functions P(m)=χ(mK_F) of 2-dimensional foliated canonical models with fixed K_F², K_F ⋅ K_X and i_ℚ(F) is finite. As a consequence, we deduce that two results on the effective birationality and boundedness of foliated canonical models with fixed Hilbert function still hold when only K_F², K_F ⋅ K_X and i_ℚ(F) are fixed. We then give examples further investigating the properties of families of canonical models, and study particular cases in which some of the conditions are not necessary.

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• Effective positivity of Hodge bundles and applications

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