TL;DR
This paper introduces affine subspace concentration conditions for lattice polytopes, proving their validity for smooth and reflexive polytopes with barycenter at the origin, using stability of tangent bundle extensions on Fano toric varieties.
Contribution
It establishes new affine subspace concentration conditions for specific lattice polytopes and connects them to stability properties of tangent bundles on Fano toric varieties.
Findings
Affine subspace concentration conditions hold for smooth and reflexive polytopes with barycenter at the origin.
Proof involves slope stability of tangent bundle extensions on Fano toric varieties.
Provides a new geometric criterion related to lattice polytopes and toric varieties.
Abstract
We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold for smooth and reflexive polytopes with barycenter at the origin. Our proof involves considering the slope stability of the canonical extension of the tangent bundle by the trivial line bundle and with the extension class on Fano toric varieties.
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