PreprintCC BY 4.0arXiv
Kawamata--Miyaoka type inequality for varieties with nef anticanonical divisor
Abstract
Let X be an ε-lc projective variety of dimension n≥ 2 such that −KX is nef and 0<ε≤ 1 is a real number. Then for any nef divisors D1,…,Dn−2, c1(X)2· D1⋯ Dn−2≤ (2(1+ε))/ε ĉ2(X)· D1⋯ Dn−2. In particular, there exists a Kawamata--Miyaoka type inequality c1(X)n≤ (2(1+ε))/ε ĉ2(X)· c1(X)n−2.
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BibTeX
@misc{liu2026kawamatamiyaoka,
title = {{Kawamata--Miyaoka type inequality for varieties with nef anticanonical divisor}},
author = {Haidong Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26597},
eprint = {2608.26597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26597},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kawamata--Miyaoka type inequality for varieties with nef anticanonical divisor
AU - Haidong Liu
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2608.26597
UR - https://arxiv.org/abs/2608.26597
AB - Let X be an ε-lc projective variety of dimension n≥ 2 such that −K_X is nef and 0<ε≤ 1 is a real number. Then for any nef divisors D_1,…,D_n−2, c_1(X)^2· D_1⋯ D_n−2≤ (2(1+ε))/ε ĉ_2(X)· D_1⋯ D_n−2. In particular, there exists a Kawamata--Miyaoka type inequality c_1(X)^n≤ (2(1+ε))/ε ĉ_2(X)· c_1(X)^n−2.
ER -