The $\chi_y$-genus, Chern number inequalities and signature

Ping Li; Yibo Ren

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arXiv · 2603.27964

The $\chi_y$-genus, Chern number inequalities and signature

Ping Li·Yibo Ren

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Abstract

This article has two parts. In the first part we introduce two positivity conditions for the modified $\chi_y$-genus on almost-complex manifolds and show that each of them implies a family of optimal Chern number inequalities. It turns out that many important K\"{a}hler and symplectic manifolds satisfy either of the two positivity conditions, and hence these Chern number inequalities hold true on them. In the second part we focus on the signature, a special value of the $\chi_y$-genus, of symplectic manifolds equipped with symplectic circle actions and give applications. Our results in this part unify and generalize various related results in the existing literature.

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Ping Li, Yibo Ren. 2026-03-30. The $\chi_y$-genus, Chern number inequalities and signature. https://arxiv.org/abs/2603.27964

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