Higher-dimensional foliated Mori theory

2019/11/14 by Calum Spicer · 9 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.1112/s0010437x19007681

Abstract

We develop some foundational results in a higher-dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman–Mori cone of curves in terms of the numerical properties of K_F for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program (MMP) for rank 2 foliations on threefolds.

Cited by

• On invariance of plurigenera for foliated surface pairs
• Explicit bounds on foliated surfaces and the Poincaré problem
• Positivity of the Moduli Part
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• Towards classification of codimension 1 foliations on threefolds of\n general type
• Codimension 1 foliations with numerically trivial canonical class on singular spaces
• On base point freeness for rank one foliations
• MMP for generalized foliated threefolds of rank one
• Counterexamples to the MMP for 1-foliations in positive characteristic. [europepmc]
• Foliation adjunction. [europepmc]

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• On The Log Sarkisov Program For Foliations On Projective 3-Folds
• Sarkisov program for algebraically integrable and threefold foliations
• MMP for generalized foliated threefolds of rank one
• Towards a Mori theory on compact Kähler threefolds, II