Holomorphic and Symplectic fillings on positive and null Sasaki 5-manifolds

Acronym

P_HSF-S5

Consortium Coordinator

Cuadros Valle, Jaime

Start Date

March 15, 2016

End Date

March 15, 2017

Status

https://purl.org/pe-repo/concytec/estadoProyecto#concluido

Tipo de proyecto

https://purl.org/pe-repo/ocde/tipoProyecto#investigacionBasica

Description

Please see file Anexo for a detailed explanation of certain definitions. It is known that many contact manifolds admit symplectic fillings, that is, they can be realized as boundary of compact symplectic manifolds. It is also known that one can extend this definition at the level of complex geometry. In this situation the analogue is given holomorphic fillings:a compact complex manifold (N,J) is a holomorphic filling of the contact manifold (M, D) if N (M,J) is strictly pseudo-convex and $D=TMcap JTM$. Due to a result of Marinescu, G., Yeganefer, N (see [MY]) Sasakian manifolds, which are of contact type, admit holomorphic fillings and thus Kählerian fillings. There is classification of Sasakian manifolds in terms of the basic Chern class (one obtains positive, negative and null structures). We are interested in simply connected 5 manifolds admitting both positive and null structures. Positive Sasakian manifolds usually can be realized as S^1-Seifert bundles over a log Del Pezzo surfaces. In the null case, they are S^1-Seifert bundles over K3 orbifolds. We think, for certain cases: it is possible to determine the (strong) symplectic filling of associated to the null case and the holomorphic filling of the positive case. The reason to choose these two structures is trying to understand an interesting connection discovered by Alexeev and Nikulin in the classification of certain Del Pezzo surfaces using K3 lattice theory. We expect to reinterpret this connection at the level of fillings.

Keywords

Variedades de Sasaki

;

Rellenos holomorfos

;

Rellenos simplécticos

;

Geometría diferencial

Área de conocimiento

Natural sciences

Campo OCDE

https://purl.org/pe-repo/ocde/ford#1.01.01