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math.AG2021
Slope inequalities for KSB-stable and K-stable families
Giulio Codogni, Luca Tasin, Filippo Viviani
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…
math.AG2021
A note on families of K-semistable log-Fano pairs
Giulio Codogni, Zsolt Patakfalvi
In this short note, we give an alternative proof of the semipositivity of the Chow-Mumford line bundle for families of K-semistable log-Fano pairs, and of the nefness threeshold fo…