Related papers: Lefschetz fibrations with infinitely many sections
Let $f:X \rightarrow \Delta $ be a one-parameter semistable degeneration of $m$-dimensional compact complex manifolds. Assume that each component of the central fiber $X_0$ is K\"ahler. Then, we provide a criterion for a general fiber to…
Novikov's theorem is a rigidity result on the class of taut foliations on three-manifolds. For higher dimensional manifolds, foliations with a strong symplectic form have been suggested as the class of foliations having similar rigidity…
We realize higher-form symmetries in F-theory compactifications on non-compact elliptically fibered Calabi-Yau manifolds. Central to this endeavour is the topology of the boundary of the non-compact elliptic fibration, as well as the…
We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of…
To a symplectic Lefschetz pencil on a monotone symplectic manifold, we associate an algebraic structure, which is a pencil of categories in the sense of noncommutative geometry. One fibre of this "noncommutative pencil" is related to the…
The Gromov-Witten theory of threefolds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invariants of a K3 surface. Toward a generalization of this result…
This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which…
We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K.~Pak, "Transversal harmonic theory for transversally symplectic flows", J. Aust.…
We give a generalization of the concept of near-symplectic structures to 2n dimensions. According to our definition, a closed 2-form \omega on a 2n-manifold M is near-symplectic, if it is symplectic outside a submanifold Z of codimension 3,…
We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP^2 # p (-CP^2) for p=7, 8, 9, and to 3 CP^2 #q (-CP^2) for q =12,...,19. Complementarily,…
For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also…
We compare different constructions of mirrors of del Pezzo surfaces, focusing on degree $d \leq 3$. In particular, we extract Lefschetz fibrations, with associated exceptional collections, from the mirrors obtained via the Hori-Vafa and…
A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth…
We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of…
It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomorphism. Moreover the former admit infinitely many…
In this article, we generalize the results discussed in [arXiv:1004.3762] by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with…
We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature.…
Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle,…
In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2-sphere. (2) There exists a minimal elliptic fibration over the 2-disk, which is not…
We show that every de Rham cohomology class on the total space of a symplectic fiber bundle with closed Lefschetz fibers, admits a Poisson harmonic representative in the sense of Brylinski. The proof is based on a new characterization of…