Tīmeklis2016. gada 4. dec. · 最近Abouzaid发展了Fukaya的想法对于存在Lagrangian torus fibration (without singular fiber)的辛流形 M\rightarrow B ，如果 \pi_2(B)=0 ，可以定 … TīmeklisGeometrically this means that, locally around the regular value c, the map f: M → R n collecting the integrals of motion is a Lagrangian fibration, i.e. it is locally trivial and the fibres are Lagrangian submanifolds. Furthermore, one also shows that the connected components of f − 1 ( c) are of the form R n − k × T k, where 0 ≤ k ≤ ...
Articles HyperK
TīmeklisLet π:X→Pn be a (holomorphic) Lagrangian fibration that is very general in the moduli space of Lagrangian fibrations. We conjecture that the singular fibres in codimension one must be semistable degenerations of abelian varieties. We prove a partial result towards this conjecture, and describe an example that provides further evidence. A Lagrangian fibration of a symplectic manifold M is a fibration where all of the fibres are Lagrangian submanifolds. Since M is even-dimensional we can take local coordinates (p1,…,pn, q ,…,q ), and by Darboux's theorem the symplectic form ω can be, at least locally, written as ω = ∑ dpk ∧ dq , where d denotes the exterior derivative and ∧ denotes the exterior product. This form is called the Poincaré two-form or the canonical two-form. Using this set-up we can locally think of M as bein… inconsistency\\u0027s nj
What is a Lagrangian submanifold intuitively? - MathOverflow
Tīmeklis2013. gada 3. jūl. · A Lagrangian fibration on X is a fibration f:X→B such that every irreducible component of every fiber of f is a Lagrangian subvariety with respect to the holomorphic symplectic form σ. To make this note more self-contained, we collect some known results concerning fibrations on hyperkähler manifolds, which we will use in … Tīmeklis2024. gada 22. maijs · Consider a Lagrangian section C of this fibration, locally written as y(x), in X. Using the identification with the cotangent bundle and the fact that C is Lagrangian with respect to $\omega $ if and only if it is closed and hence locally exact, it is shown [ 8 ] that locally Tīmeklis2024. gada 16. marts · This paper deals with Lagrangian fibrations in coupled resonant oscillators containing swinging spring oscillators of four degrees of freedom. We will … inconsistency\\u0027s nr