Related papers: Symplectic blowing down in dimension Six
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical…
The symplectic projector method is applied to derive the local physical degrees of freedom of a particle moving freely on an arbitrary surface. The dependence of the projector on the coordinates and momenta of the particle is discussed.
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…
We construct a sequence of explicit blow-ups and blow-downs on irreducible compact Hermitian symmetric spaces $X$ which transforms it into a projective space of the same dimension. Moreover this resolves a birational map given by Landsberg…
The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are…
A conformal factor in the Bohr model embeds Bohr space in six dimensions, revealing the $O(6)$ symmetry and its contraction to the $E(5)$ at infinity. Phenomenological consequences are discussed after the re-formulation of the Bohr…
For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan,…
In this paper a novel criterion for the slicing of the jump set of a function is provided, which bypasses the codimension-one and the parallelogram law techniques developed in $BD$-spaces. The approach builds upon a recent rectifiability…
This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing--up, to arbitrary characteristic.
A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…
Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e. over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove that, under…
In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the…
Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…
Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition.…
We give a method to obtain new 7-dimensional Lie algebras endowed with closed and coclosed G2-structures starting from 6-dimensional Lie algebras with symplectic half- at SU(3)-structures and half- at SU(3)- structures, respectively.…
We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic…