Holomorphic Morse inequalities for orbifolds

TL;DR

This paper extends holomorphic Morse inequalities to complex orbifolds using heat kernel methods and introduces Moishezon orbifolds, providing a geometric criterion for their characterization, thus generalizing classical results to orbifolds.

Contribution

It proves Demailly's holomorphic Morse inequalities for orbifolds and introduces Moishezon orbifolds, broadening the applicability of these inequalities and criteria.

Findings

Holomorphic Morse inequalities hold for orbifolds.

Introduction of Moishezon orbifolds and their characterization.

Generalization of Grauert-Riemenschneider conjecture results to orbifolds.

Abstract

We prove that Demailly's holomorphic Morse inequalities hold true for complex orbifolds by using a heat kernel method. Then we introduce the class of Moishezon orbifolds and as an application of our inequalties, we give a geometric criterion for a compact connected orbifold to be a Moishezon orbifolds, thus generalizing Siu's and Demailly's answers to the Grauert-Riemenschneider conjecture to the orbifold case.