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Minimising CM degree and slope stability of projective varieties
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2021-02-24 , DOI: 10.1017/s0305004121000141
KENTARO OHNO

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.

中文翻译:

最小化投影品种的CM度和坡度稳定性

我们讨论了 Chow-Mumford (CM) 线束在具有固定一般纤维的极化家族的所有可能填充中的最小化问题,其动机是研究 K 稳定 Fano 变体的模空间。我们表明,如果中心纤维是光滑的,这种最小化意味着纤维的斜率半稳定性。
更新日期:2021-02-24
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