Questions tagged [differential-forms]
A differential form $ \omega$ is a section of the exterior algebra $\Lambda^* T^* X$ of a cotangent bundle,
112 questions
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Restriction of a line bundle to a two-cycle
I am reading a paper on Chiral Differential Operators
http://arxiv.org/pdf/hep-th/0604179v3.pdf
and it says on page 23 that a line bundle over a manifold C can be characterized completely by its ...
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(n-1)-dimensional normal currents and Smirnov's paper
I don't know much about currents, but I saw a paper of Smirnov which seems relevant to a problem I am working on. In the very last paragraph of page 848 of the following paper
http://www.unige.ch/~...
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Integrability at $z$ of the 2-form $ d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta} $
Given $g\in\mathcal{C}^1(\bar\Delta)$, and $z\in\Delta$, how can i prove that the 2-form
$$
d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta}
$$
is integrable in $z$?
At ...
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Homology of a region of the plane
This is related to this MO question, I don't know if it's really "research-level". As in that question, let $U$ be a domain of the complex plane $\mathbb{C}$, i.e. an open connected subset. Let
$$ \...
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Differential ideals of Pfaffian forms on jet bundles (Integrability)
(I asked this question on math.stackexchange, but got no reaction in several weeks. So, my conclusion is, that it is harder to answer than I thought, and maybe admissible for the attribute 'research ...
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Interpolating from a Hard Lefschetz class to a Kaehler class
Let $X$ be a compact smooth manifold that admits symplectic and Kaehler structures.
There is a paper by Ugarte, Rudyak, Tralle, and Ibanez, showing how the Lefschetz rank can vary along a path of ...
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Analytic version of the Cartan lemma
Assume that $\beta$ is a real analytic 2-form on an analytic manifold $M$ and $\alpha$ is an analytic non vanishing 1-form on $M$. Assume that $\beta \wedge \alpha=0$. Is there an analytic 1-form $\...
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Residues and Mittag-Leffler sequence
Let $X$ be a compact Riemann surface, $\omega$ a meromorphic differential on $X$ and $f$ a meromorphic function on $X$ with poles only over the points $P_1,\dots,P_d$. The product $\;f\cdot\omega\;$ ...
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existence of meromorphic differentials with non vanishing residues
Let $X$ be a smooth projective variety over a field $k$ of characteristic zero and let $D$ be a simple normal crossing divisor on $X$, with irreducible components $D_i$.
Does there exist a nonzero ...
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differential forms in double field theory
In double field theory, there are 'double differential forms' meaning that the standard 1-forms $d x^i$ generate an algebra over functions depending on both of the double coordinates
$x^i$ and $\tilde ...
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superdiff forms and tensors
Where is it written that symmetric tensors (i.e. with multiindices)
occur as the coefficient functions of super differential forms
or rather odd differential forms?
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Application of $k$-forms to differential equations
I was presented with a problem that, in my view, is somewhat difficult, and it relates $k$-forms to systems of differential equations.
Consider the ellipsoid, given by
$$f(u, v)=(a\sin(u) \cos(v), b \...
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