# Morse-type integrals on non-K\"ahler manifolds

## TL;DR

This paper investigates Morse-type integrals on non-Kähler manifolds, proposing a conjecture for nef (1,1) classes and proving it under specific positivity and metric conditions.

## Contribution

It introduces a conjecture about Morse-type integrals on nef classes and proves it in special cases involving semipositivity and particular Hermitian metrics.

## Key findings

- Conjecture holds for semipositive classes.
- Conjecture verified when the manifold admits certain Hermitian metrics.
- Provides new insights into Morse-type integrals on non-Kähler manifolds.

## Abstract

We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics.