Related papers: Laminations from the symplectic double
In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction this is a natural…
In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula…
We prove that the morphism that maps a rational ruled surface to its singular locus is genericaly injective modulo isomophism and duality. We also calculate the dimension and the degre of its image.
We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the…
We study symplectic Laplacians on compact symplectic manifolds with boundary. These Laplacians are associated with symplectic cohomologies of differential forms and can be of fourth-order. We introduce several natural boundary conditions on…
Friedman and Morgan made the "speculation" that deformation equivalence and diffeomorphism should coincide for algebraic surfaces. Counterexamples, for the hitherto open case of surfaces of general type, have been given in the last years by…
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we…
This paper studies the geometry of Cartan-Hartogs domains from the symplectic point of view. Inspired by duality between compact and noncompact Hermitian symmetric spaces, we construct a dual counterpart of Cartan-Hartogs domains and give…
We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…
A convex lattice polygon Delta determines a pair (S,L) of a toric surface together with an ample toric line bundle on S. The Severi degree N^{Delta,delta} is the number of delta-nodal curves in the complete linear system |L| passing through…
This paper considers the enhanced symplectic "category" for purposes of quantizing quasi-Hamiltonian $G$-spaces, where $G$ is a compact simple Lie group. Our starting point is the well-acknowledged analogy between the cotangent bundle…
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic…
We give a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. The main result of this article is the proof that the topological…
Hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators. Here we show that hermitian symplectic spaces may also be used to describe the solution to the factorisation problem for the scattering…
The symplectic isotopy conjecture states that every smooth symplectic surface in $CP^2$ is symplectically isotopic to a complex algebraic curve. Progress began with Gromov's pseudoholomorphic curves [Gro85], and progressed further…
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the K\"{a}hler cone of the latter. We then propose a version of mirror symmetry…
We present a new proof of the bi-Lipschitz model theorem, which occupies the main part of the Ending Lamination Conjecture proved by Minsky and Brock-Canary-Minsky. Our proof is done by using techniques of standard hyperbolic geometry as…
We are interested in expanding our understanding of symplectic matroids by exploring the properties of a class of symplectic matroids with a "lattice of flats". Taking a well-behaved family of subdivisions of the cross polytope we obtain a…