Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov Brendan Hassett & Yuri Tschinkel

Author:Fedor Bogomolov, Brendan Hassett & Yuri Tschinkel
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Let X be a projective manifold. Given a non-trivial numerical curve class , we are interested in the set of classes whose induced Harder–Narasimhan filtration of the tangent bundle agrees with that of α,

The decomposition of the movable cone into disjoint subsets of the form Δ α , called “destabilising chambers”, was studied in the 2010 Freiburg thesis of Sebastian Neumann. He obtained the following two results.

Theorem 3.22 (Decomposition of the moving cone, [26, Theorem 3.3.4, Proposition 3.3.5]).

Let X be a projective manifold. The destabilising chambers are convex cones whose closures are locally polyhedral in the interior of Mov (X). The decomposition of the moving cone is locally finite in the interior of Mov (X). If we assume additionally that the cone of movable curves is polyhedral, then the chamber structure is finite.

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