Related papers: Lefschetz fibrations on compact Stein surfaces

We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with…

We prove a Lefschetz hypersurface theorem for abelian fundamental groups allowing wild ramification along some divisor. In fact, we show that isomorphism holds if the degree of the hypersurface is large relative to the ramification along…

In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz…

We show that there are no non-trivial stratified bundles over a smooth simply connected quasi-projective variety over the algebraic closure of a finite field, if the variety admits a normal projective compactification with boundary locus of…

Let $M$ be a Liouville 6-manifold which is the smooth fiber of a Lefschetz fibration on $\mathbb{C}^4$ constructed by suspending a Lefschetz fibration on $\mathbb{C}^3$. We prove that for many examples including stabilizations of Milnor…

It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable…

A bifibration structure on a $6$-manifold is a map to either the complex projective plane $\mathbb{P}^2$ or a $\mathbb{P}^1$-bundle over $\mathbb{P}^1$, such that its composition with the projection to $\mathbb{P}^1$ is a ($6$-dimensional)…

The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share…

We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact 4-dimensional Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit…

Given two hyperbolic surfaces and a homotopy class of maps between them, Thurston proved that there always exists a representative minimizing the Lipschitz constant. While not unique, these minimizers are rigid along a geodesic lamination.…

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection has…

We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard…

We study the Noether-Lefschetz locus of a very ample line bundle L on an arbitrary smooth threefold Y. Building on results of Green, Voisin and Otwinowska, we give explicit bounds, depending only on the Castelnuovo-Mumford regularity…

We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a…

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…

I prove "Lefschetz principle"-type theorems for semistable and curve semistable Higgs sheaves on smooth projective varieties defined over an algebraically closed field of characteristic $0$. These theorems are applied to reduce a…

We show that the combination of nonnegative 2-intermediate Ricci Curvature and strict positivity of scalar curvature forces rigidity of two-sided free boundary stable minimal hypersurface in a 4-manifold with bounded geometry and weakly…

Let $F$ be a transversely oriented foliation of codimension 1 on a closed manifold $M$, and let $\phi=\{\phi^t\}$ be a foliated flow on $(M,F)$. Assume the closed orbits of $\phi$ are simple and its preserved leaves are transversely simple.…

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…

Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration can be…