Locally conformal symplectic blow-ups

TL;DR

This paper demonstrates that the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold admits a compatible locally conformal symplectic structure, extending the geometric understanding of such manifolds.

Contribution

It introduces a method to construct locally conformal symplectic structures on blow-ups along symplectic submanifolds, a new result in symplectic geometry.

Findings

Existence of locally conformal symplectic structures on blow-ups

Extension of symplectic blow-up techniques to conformal setting

New insights into the geometry of locally conformal symplectic manifolds

Abstract

In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.