The lagrangian-submanifolds tag has no wiki summary.
3
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1answer
149 views
Special Lagrangians and fat
I am unable to find the MO comments about the first use of the phrase "fat slags" in an article. On page 26 of this we find "these correspond to thickenings of the
corresponding special Lagrangian ...
6
votes
2answers
252 views
How many Lagrangian submanifolds?
An $n$-dimensional submanifold $L$ of a symplectic manifold $(M^{2n}, \omega)$ is called Lagrangian if $\omega|_L = 0$. I want to get some feeling about how many Lagrangian submanifolds are.
For each ...
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0answers
107 views
When a hyperplane of symmetric forms is determined by a quadric hypersurface?
Let $L$ be a 2D real vector space, $L^*$ its dual, and $\{V,\omega\}$ the symplectic space with $V=L\oplus L^*$ and $\omega$ unambiguously defined by $\omega(l,\lambda):=\lambda(l)$, for all $l\in L$ ...
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2answers
515 views
about decomposition of three forms
Patrick D. Baier in his Ph.D. thesis for proving the theorem 2.1.4 used the following non-trivial fact (in chapter 2 on page 14):
Let $0\neq X\in V$ (here $V$ is of dimension 6), $W^\ast = Ann(X)$ ...
6
votes
1answer
356 views
For which Calabi-Yau threefolds is SYZ conjecture known to hold?
I would like to know for which Calabi-Yau threefolds SYZ conjecture is known to hold. I am aware of works by Gross-Wilson (Borcea-Voisin CY3s) and Ruan (quintic CY3), but they are quite classical ...
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0answers
162 views
Image of an isotropic manifold under lagrangian correspondence is isotropic?
Is the following statement well known?
Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth)
Lagrangian correspondence. For a subset $X \subset M$ we denote ...
3
votes
3answers
282 views
Lagrangian Kleinian bottles
I remember some talks some time ago about proofs of nonexistence of Lagrangian Kleinian bottles in C^2 for the standard symplectic structure, mentioning that this were the only compact surface for ...
1
vote
1answer
295 views
holomorphic sections on elliptic K3 surface
Hi all,
I want to ask something about the holomorphic sections on elliptic K3:
Is there any obstruction for an ellptic K3 (as an elliptic fibration) to have holomorphic sections? Is that always some ...
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0answers
174 views
Co-normal bundle of orthogonal compliment
Is the following fact well known?
Let $X$ be a manifold and $V$ be a vector space. Let $E_1$ be a sub-bundle of the constant bundle $X \times V$. Let $E_2$ be its orthogonal compliment in $X ...
4
votes
1answer
896 views
Cohomology theory for symplectic manifolds
Suppose I have a symplectic manifold $(M,\omega)$ and a line bundle $\mathcal L$ with a connection with curvature $\omega$ (or perhaps it's more standard to say $\frac i{2\pi}\omega$; anyway, the ...
4
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1answer
304 views
Direct image of Lagrangian subspaces of the co-tangent bundle:
Let p:X \to Y be a map of smooth algebraic varieties.
Let $C \subset T^\* X$ be a (locally closed) submanifold. Denote by $p_\*(C) \subset T^\* Y$ the following set:
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
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2answers
774 views
Lagrangian Submanifolds in Deformation Quantization
Suppose I have a symplectic manifold $M$, and have a deformation quantization of it, i.e. an associative product $\ast:C(M)[[\hbar]]\otimes C(M)[[\hbar]]\to C(M)[[\hbar]]$ so that $f\ast ...
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0answers
435 views
Are there cohomology classes on a hyperkähler manifolds which pull back to the Stiefel-Whitney classes on every Lagrangian submanifold?
This is a bit of a stab in the dark but I was wondering if anyone has defined cohomology classes on a hyperkähler manifold which pull back to the Stiefel-Whitney classes on any submanifold which is ...
