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Minimising CM degree and slope stability of projective varieties

Part of: Families, fibrations Complex manifolds

Published online by Cambridge University Press:  24 February 2021

KENTARO OHNO
KENTARO OHNO*
Affiliation:
Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan e-mail: [email protected]
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Abstract

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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.

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Secondary: 32Q26: Notions of stability
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 125 - 137
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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