Embedding theorems for quasi-toric manifolds given by combinatorial data

V. M. Buchstaber^a, A. A. Kustarev<sup>b

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences
^b Faculty of Computer Science, National Research University "Higher School of Economics"

Abstract: This paper is devoted to problems on equivariant embeddings of quasi-toric manifolds in Euclidean and projective spaces. We construct explicit embeddings and give bounds for the dimensions of the embeddings in terms of combinatorial data that determine such manifolds. We show how familiar results on complex projective varieties in toric geometry can be obtained under additional restrictions on the combinatorial data.

Keywords: equivariant embedding, moment-angle manifold, characteristic function.

UDC: 515.165.2

MSC: 57S15, 57R20

Received: 28.11.2015

DOI: 10.4213/im8399

 English version: Izvestiya: Mathematics, 2015, 79:6, 1157–1183

Bibliographic databases:

• 
• 
• 
• 
• 
•