Details
| Original language | English |
|---|---|
| Pages (from-to) | 1029-1050 |
| Number of pages | 22 |
| Journal | Revista Matematica Iberoamericana |
| Volume | 38 |
| Issue number | 3 |
| Publication status | Published - 26 Jan 2022 |
Abstract
Keywords
- math.DG, math.AG, math.SG, 53C25, 53D35, 14J28, 14J17, cyclic orbifold, K-contact, K3 surface, Sasakian, Smale–Barden manifold
ASJC Scopus subject areas
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In: Revista Matematica Iberoamericana, Vol. 38, No. 3, 26.01.2022, p. 1029-1050.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quasi-regular sasakian and K-contact structures on smale-barden manifolds
AU - Cañas, Alejandro
AU - Muñoz, Vicente
AU - Schütt, Matthias
AU - Tralle, Aleksy
N1 - Funding Information: Funding. The first author is supported by a PhD grant from Universidad de Málaga. The second author was partially supported by Project MINECO (Spain) PGC2018-095448-BI00. The fourth author was supported by the National Science Center (Poland), grant NCN no. 2018/31/B/ST1/00053.
PY - 2022/1/26
Y1 - 2022/1/26
N2 - Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Koll\'ar). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic K\"ahler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with b1=0 and b2>1 there cannot be b2 smooth disjoint complex curves of genus g>0 spanning the (rational) homology.
AB - Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Koll\'ar). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic K\"ahler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with b1=0 and b2>1 there cannot be b2 smooth disjoint complex curves of genus g>0 spanning the (rational) homology.
KW - math.DG
KW - math.AG
KW - math.SG
KW - 53C25, 53D35, 14J28, 14J17
KW - cyclic orbifold
KW - K-contact
KW - K3 surface
KW - Sasakian
KW - Smale–Barden manifold
UR - http://www.scopus.com/inward/record.url?scp=85130449871&partnerID=8YFLogxK
U2 - 10.4171/RMI/1335
DO - 10.4171/RMI/1335
M3 - Article
VL - 38
SP - 1029
EP - 1050
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
SN - 0213-2230
IS - 3
ER -