Symplectic log Calabi-Yau surface---deformation class

Li, Tianjun; Mak, Cheuk Yu

doi:10.48550/arxiv.1510.06131

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Contact Kodaira Dimensions For Some Fibered Manifolds1

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Cited by 2 publications

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“…Moreover, c 1 | P is torsion and the Poincare dual of c 1 | N (D) is represented by D (this can be checked by adjunction) implies that D represents the Poincare dual of the first Chern class in (X, ω) and hence a symplectic Looijenga pair in the sense of [22]. By the classification result in [22], the embeddability of D as a symplectic divisor in a symplectic rational manifold is the same as that in the complex (Kähler) case. By the assumption that D is not embeddable in the complex sense, we get a contradiction.…”

Section: Contact Kodaira Dimensions For Some Fibered Manifoldsmentioning

confidence: 99%

The Kodaira Dimension of Contact 3-Manifolds and Geography of Symplectic Fillings

Mak

2018

International Mathematics Research Notices

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We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. In particular, contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of fillings. On the other hand, we also prove that, given any contact 3-manifold, there is a lower bound of 2χ + 3σ for all its minimal symplectic fillings. This is motivated by Stipsicz's result in [38] for Stein fillings. Finally, we discuss various aspects of exact self cobordisms of fillable 3-manifolds.

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Section: Contact Kodaira Dimensions For Some Fibered Manifoldsmentioning

confidence: 99%