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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 6, Pages 65–92 (Mi izv8399)  

Embedding theorems for quasi-toric manifolds given by combinatorial data

V. M. Buchstabera, A. A. Kustarevb

a 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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00414
This work was supported by the Russian Science Foundation under grant no. 14-11-00414.


DOI: https://doi.org/10.4213/im8399

Full text: PDF file (644 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:6, 1157–1183

Bibliographic databases:

UDC: 515.165.2
MSC: 57S15, 57R20
Received: 28.11.2015

Citation: V. M. Buchstaber, A. A. Kustarev, “Embedding theorems for quasi-toric manifolds given by combinatorial data”, Izv. RAN. Ser. Mat., 79:6 (2015), 65–92; Izv. Math., 79:6 (2015), 1157–1183

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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