Complex-analytic structures on moment-angle manifolds

Panov, Taras; Ustinovsky, Yuri

doi:10.48550/arxiv.1008.4764

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Lagrangian Embeddings and Moment-angle Manifolds1

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2013

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“…Theorem 4.3 (see [BM,Lemma 0.12] or [PU,Theorem 4.3]). The intersections of quadrics (2.1) and (2.2) are nondegenerate and nonempty if and only if presentation (4.2) is generic.…”

Section: Lagrangian Embeddings and Moment-angle Manifoldsmentioning

confidence: 99%

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

Mironov

Panov

2013

Funct Anal Its Appl

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Abstract. We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of N : every N embeds as a submanifold in the corresponding moment-angle manifold Z, and every N is the total space of two different fibrations, one over the torus T m−n with fibre a real moment-angle manifold R, and the other over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.

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“…Theorem 4.3 (see [BM,Lemma 0.12] or [PU,Theorem 4.3]). The intersections of quadrics (2.1) and (2.2) are nondegenerate and nonempty if and only if presentation (4.2) is generic.…”

Section: Lagrangian Embeddings and Moment-angle Manifoldsmentioning

confidence: 99%

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

Mironov

Panov

2013

Funct Anal Its Appl

View full text Add to dashboard Cite

show abstract

Complex-analytic structures on moment-angle manifolds

Cited by 1 publication

References 12 publications

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

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