On the blow-up formula of the Chow weights for polarized toric manifolds

2024/07/14 by King Leung Lee, Lee, King Leung, Naoto Yotsutani +1
Mathematics · #14M25 #51M20 #53C55 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2407.10082

openalex publication_date 2024/07/14 · openalex created_date 2024/07/17 · openalex updated_date 2026/08/01

Abstract

Let X be a smooth projective toric variety, and let \widetildeX denote the blow-up of X at finitely many distinct torus-invariant points. In this paper, we derive an explicit combinatorial formula for the Chow weight of \widetildeX in terms of the underlying toric manifold X and the symplectic cuts of its associated Delzant polytope. As an application, we study toric blow-ups of the projective plane and compare their Chow stability with that of blow-ups at general points.

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• Logarithmic Chow semistability of polarized toric manifolds
• Unstable Blowups