Minimising CM degree and slope stability of projective varieties

We discuss a minimisation problem of the degree of the Chow–Mumford (CM) line bundle among all possible fillings of a polarised family with fixed general fibers, motivated by the study of the moduli space of K-stable Fano varieties. We show that such minimisation implies the slope semistability of t...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2022-01, Vol.172 (1), p.125-137
Main Author: OHNO, KENTARO
Format: Article
Language:English
Subjects:
Inequality
Optimization
Slope stability
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Summary:We discuss a minimisation problem of the degree of the Chow–Mumford (CM) line bundle among all possible fillings of a polarised family with fixed general fibers, motivated by the study of the moduli space of K-stable Fano varieties. We show that such minimisation implies the slope semistability of the fiber if the central fiber is smooth.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004121000141