Minimizing CM degree and slope stability of projective varieties

2018/11/29 by Ohno, Kentaro
#14D20 #32Q26 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.12229

Abstract

We discuss a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family with fixed general fibers. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

Related

• Minimizing CM degree and specially K-stable varieties
• Positivity of the CM line bundle for families of K-stable klt Fano\n varieties
• CM Stability of Projective varieties
• CM-line bundles and slope \K-semistability for big and nef line bundles along subschemes
• Equivariant CM minimization for extremal manifolds