Duistermaat-Heckman formula for a torus action on a generalized Calabi-Yau manifold and localization formula

TL;DR

This paper extends previous work on Hamiltonian actions on generalized Calabi-Yau manifolds by demonstrating that the Duistermaat-Heckman measure density is piecewise polynomial and confirming the localization formula.

Contribution

It proves the piecewise polynomial nature of the Duistermaat-Heckman measure density and verifies the localization formula for generalized Calabi-Yau manifolds.

Findings

Density function of the Duistermaat-Heckman measure is piecewise polynomial.

Localization formula holds for the studied manifold.

Extends Duistermaat-Heckman theorem to generalized Calabi-Yau settings.

Abstract

This note is an addendum to our earlier work \cite{humi}. In \cite{humi}, we studied a Hamiltonian action for a generalized Calabi-Yau manifold and showed that the Duistermaat-Heckman theorem holds. The purpose of this note is to show that the density function of the Duistermaa-Heckman measure is a piecewise polynomial. We also prove that the localization formula holds.