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Minimising CM degree and slope stability of projective varieties
Published online by Cambridge University Press: 24 February 2021
Abstract
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
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 125 - 137
- Creative Commons
- 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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