A note on Teissier problem for nef classes

Zhang, Yashan

doi:10.1090/proc/16738

A note on Teissier problem for nef classes
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by Yashan Zhang;

Proc. Amer. Math. Soc. 152 (2024), 2831-2843

DOI: https://doi.org/10.1090/proc/16738

Published electronically: May 7, 2024

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Abstract:

Teissier problem aims to characterize the equality case of Khovanskii-Teissier type inequality for $(1,1)$-classes on a compact Kähler manifold. When each of the involved $(1,1)$-classes is assumed to be nef and big, this problem has been solved by the previous works of Boucksom-Favre-Jonsson [J. Algebraic Geom. 18 (2009), pp. 279–308], Fu-Xiao [Algebr. Geom. 6 (2019), pp. 177–185] and Li [The Alexandrov-Fenchel type inequalities, revisited, https://arxiv.org/abs/1710.00520]. In this note, we shall settle the case that the involved $(1,1)$-classes are just assumed to be nef. We also extend the results to some settings where some of the $(1,1)$-classes are not necessarily nef. By constructing examples, it is shown that our results are optimal.

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