Questions tagged [cotangent-bundles]
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17 questions with no upvoted or accepted answers
15
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0
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334
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Beyond smoothness-the clear picture about the notion of a differential form
In this paper N.Teleman constructs the signature operator on an arbitrary (closed, oriented) Lipschitz manifold with coefficients in a vector bundle $\xi$. In particular the notion of a differential $...
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7
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253
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Triviality, ampleness, nefness, and bigness of the tangent bundle
Let $X$ be a smooth projective connected variety over $\mathbb{C}$ and let $T_X$ be its tangent bundle.
If $T_X$ is ample, then $X$ is isomorphic to a projective space by Mori's theorem.
If $T_X$ is ...
- 513
6
votes
0
answers
368
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Lagrangian up to Hamiltonian in cotangent bundle
I want to understand the folklore conjecture that, in a CY manifold, Lagrangians up to Hamiltonian isotopies are represented by special Lagrangians by examining cotangent bundle and Hodge theory.
...
- 61
3
votes
0
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99
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Displacing a conormal Lagrangian from the zero section
I was told that the conormal bundle $\nu^*K$ of a knot $K\subset S^3$ can be displaced from the zero section $0_{S^3}$ in $T^*S^3.$ Having no intuition about whether/how often this happens in general, ...
- 1,677
3
votes
0
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95
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On the degrees of the normal and tangent sheaves of Gorenstein curves in Pn
It is known that if an irreducible curve $C$ is a local complete intersection in $\mathbb{P}^n$, then
$\wedge^{n-1}\mathcal{N}\otimes\omega_{\mathbb{P}^n}$ is isomomorphic to the dualizing sheaf $\...
3
votes
0
answers
141
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Is there a precisely formulable obstruction for the tangent bundle being a Lie algebra bundle?
Although vector fields (which are sections of the tangent bundle) form Lie algebras, the bundle itself, as far as I know, almost never carries Lie algebra structure; that is, in general, I believe, ...
- 18.4k
3
votes
0
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394
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Reference for plumbing cotangent bundles as Liouville manifolds
A Liouville domain $(W, \omega,\alpha, X)$ is a compact manifold $W$ with boundary $\partial W$, and a exact symplectic structure $\omega = d\alpha, \iota_X \omega = \alpha$, such that $X$ points ...
- 316
2
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0
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157
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Is the cotangent sheaf of the symmetric product reflexive?
Let $X$ be a smooth projective surface and $X^{(n)}:= X^n/\mathfrak{S}_n$ be the nth symmetric product of $X$.
When is the cotangent sheaf of $X^{(n)}$ reflexive?
- 21
2
votes
0
answers
70
views
Schur Bundle of Smooth Manifold
I've seen hints at the following result:
Let $M$ be a 3-dimensional manifold and let $T := T^*M$ be the cotangent bundle. By Schur-Weyl Duality, the 3rd tensor product can be written as follows:
$$T^...
- 901
2
votes
0
answers
223
views
how to understand the manifold with boundary jet bundle and cotangent bundle with boundary
Suppose that $M\subset (W^{2n},\omega)$ is an $n$-dimensional manifold with smooth boundary $\partial M$, where $(W,\omega)$ is a $2n$-dimensional Kähler manifold and boundary with contact type ...
- 111
2
votes
0
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643
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A symplectic structure for cotangent bundle
Before that I mention my question explicitly, I start with my motivation:
Look at $\mathbb{D} \times \mathbb{C}=\{(x_{1},x_{2},y_{1},y_{2})\mid x_{1}^{2}+x_{2}^{2}< 1\}$.This can be identified ...
- 366
1
vote
0
answers
159
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Affinization map of cotangent bundle is proper/projective?
Given a cotangent bundle of a projective variety $Y=T^*X,$ do we know that its affinization map,
$$Y \rightarrow \mathrm{Spec}(H^0(Y,\mathscr{O}_Y))$$
is proper or projective?
- 1,677
1
vote
0
answers
189
views
Relating the Morse index with the Maslov index
In the following paper https://arxiv.org/pdf/math/0408280.pdf there is created an isomorphism between the Floer Homology of an hamiltonian functional $H$ in the cotangent bundle and the the Morse ...
- 791
1
vote
0
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309
views
Restriction of the sheaf of relative differentials
Let $f:X\rightarrow C$ be a morphism, where $C$ is a smooth curve, and let $\Omega_f$ be the sheaf of relative differentials.
For $t\in C$ let $i_t:X_t = f^{-1}(t)\rightarrow X$ be the inclusion of ...
user61586
1
vote
0
answers
221
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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 \...
- 2,649
0
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0
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98
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A question about the sheaf supported on the zero section
Let $X$ be the total space of the cotangent sheaf on $\mathbb{P}^{2}$ and $i \colon \mathbb{P}^{2} \hookrightarrow X$ be thezero section. Suppose that $E$ is a coherent sheaf on $X$ which is set-...
0
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0
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161
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Projectivization of the normal bundle of $\mathbb P^4$ in the 10-spinor variety
Let $X=S_{10} \subset \mathbb P^{15}$ be the 10-dimensional spinor variety in its minimal embedding. Consider a $\mathbb P^4 \subset S_{10}$, hence we can define the normal bundle $N=N_{\mathbb P^4|S_{...
- 381