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arXiv · 2107.09553

Slope inequalities for KSB-stable and K-stable families

Giulio Codogni·Luca Tasin·Filippo Viviani
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Abstract

We prove some higher dimensional generalizations of the slope inequality originally due to G. Xiao, and to M. Cornalba and J. Harris. We give applications to families of KSB-stable and K-stable pairs, as well as to the study of the ample cone of the moduli space of KSB-stable varieties. Our proofs relies on the study of the Harder-Narasimhan filtration, and some generalizations of Castelnuovo's and Noether's inequalities.

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Giulio Codogni, Luca Tasin, Filippo Viviani. 2021-07-20. Slope inequalities for KSB-stable and K-stable families. https://arxiv.org/abs/2107.09553

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