Related papers: Lefschetz pencils and divisors in moduli space
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated…
Given a closed symplectic manifold, we construct invariants which count (a) closed rational pseudoholomorphic curves with prescribed cusp singularities and (b) punctured rational pseudoholomorphic curves with ellipsoidal negative ends. We…
We apply ideas from conformal field theory to study symplectic four-manifolds, by using modular functors to "linearise" Lefschetz fibrations. In Chern-Simons theory this leads to the study of parabolic vector bundles of conformal blocks.…
We prove an analogue of the Lefschetz (1,1) Theorem characterizing cohomology classes of Cartier divisors (or equivalently first Chern classes of line bundles) in the second integral cohomology. Let $X$ be a normal complex projective…
We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and…
We construct two types of non-holomorphic Lefschetz fibrations over $S^2$ with $(-1)$-sections ---hence, they are fiber sum indecomposable--- by giving the corresponding positive relators. One type of the two does not satisfy the slope…
The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified…
We list up to M\"obius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils of circles, together with the number of such pencils. In addition, we classify incidences between the…
In this paper, we will show that certain types of symplectic homology can be used as an invariant of 3-dimensional Besse manifolds, which are strict contact manifolds with periodic Reeb flow. For simplicity, we will assume our Besse…
For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…
We construct rational elliptic surfaces of index two by explicitly constructing their associated Halphen pencils in the projective plane $\mathbb{P}^2$. For each of the types of singular fibers that occur we construct at least one example…
The present work is a user's guide to the results of a previous paper by the second and third authors, where a description of the space of characters of a quasi-projective variety was given in terms of global quotient orbifold pencils.…
It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field)…
For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We prove a Lefschetz-type coincidence theorem: if the Lefschetz…
After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We…
We first present the construction of the moduli space of real pseudo-holomorphic curves in a given real symplectic manifold. Then, following the approach of Gromov and Witten, we construct invariants under deformation of real rational…
Let $X$ be a del Pezzo surface. When the degree of $X$ is at least 4, we compute the cohomology of a general sheaf in the moduli space of Gieseker semistable sheaves. We also classify the Chern characters for which the general sheaf in the…
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…
In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and…
We describe symplectic mapping class relations between products of positive Dehn twists along Lagrangian spheres in Weinstein $4$-manifolds, all of which are affine $\mathbb{C}$ varieties. The relations are obtained by applying…