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The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-
Abstract
We establish the following Miyaoka-Yau inequality for any n-dimensional klt Fano variety X, possibly K-unstable, in terms of its delta invariant: (2(n+1)ĉ2(X)−n c1(X)2)· c1(X)n−2 ≥ −n (1−min{1,δ(X)})2 · c1(X)n. Moreover, if equality holds in this inequality, then there exist a finite quasi-étale cover X̂ → X and a positive integer p such that X̂ ≅ ℙ(1,…, 1, p). We also discuss the relationship between Donaldson's conjecture and the Miyaoka-Yau inequality.
Related
BibTeX
@misc{hisamoto2026miyaokayau,
title = {{The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-}},
author = {Tomoyuki Hisamoto and Masataka Iwai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.25181},
eprint = {2607.25181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25181},
}
RIS
TY - UNPB
TI - The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-
AU - Tomoyuki Hisamoto
AU - Masataka Iwai
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.25181
UR - https://arxiv.org/abs/2607.25181
AB - We establish the following Miyaoka-Yau inequality for any n-dimensional klt Fano variety X, possibly K-unstable, in terms of its delta invariant: (2(n+1)ĉ_2(X)−n c_1(X)^2)· c_1(X)^n−2 ≥ −n (1−min{1,δ(X)})^2 · c_1(X)^n. Moreover, if equality holds in this inequality, then there exist a finite quasi-étale cover X̂ → X and a positive integer p such that X̂ ≅ ℙ(1,…, 1, p). We also discuss the relationship between Donaldson's conjecture and the Miyaoka-Yau inequality.
ER -