LVMB manifolds and quotients of toric varieties

TL;DR

This paper explores LVMB manifolds, interpreting their construction as quotients of toric manifolds by complex Lie groups, extending known classes, and answering a specific open question in the field.

Contribution

It provides a toric geometric interpretation of LVMB manifolds, extends the class of LVM manifolds, and addresses an open question posed by Cupit-Foutou and Zaffran.

Findings

LVMB manifolds can be described as quotients of toric manifolds by complex Lie groups.

The class of LVMB manifolds extends the previously known LVM manifolds.

The paper answers an open question related to the structure of these manifolds.

Abstract

In this article, we study a class of manifolds introduced by Bosio called $\LVMB$ manifolds. We provide an interpretation of his construction in terms of quotient of toric manifolds by complex Lie groups. Furthermore, $\LVMB$ manifolds extend a class of manifolds obtained by Meersseman, called $\LVM$ manifolds, and we give a characterization of these manifolds using our toric description. Finally, we give an answer to a question asked by Cupit-Foutou and Zaffran.