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revised Volume of the unitary group
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revised Volume of the unitary group
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revised Volume of the unitary group
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revised Volume of the unitary group
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revised Volume of the unitary group
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25
answered Volume of the unitary group
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Feb
15
comment space at the Planck scale
with the linearity of the classical objects. I agree that the naive proposal does not work but one has to give better reasons.
Feb
15
comment space at the Planck scale
I essentially agree with the general message of this answer, but I disagree with the objection given to the naive proposal. The linear combination $c_1M_1+c_2M_2$ can trivially be taken in the vector space generated by the $M_i$'s and it is usually this kind of thing one has to do in quantum mechanics. For example, in gauge theory, we have classically bundles-with-connections and if $E_1$ and $E_2$ are two such objects then $c_1M_1+c_2M_2$ is a well-defined element in the Hilbert space of the theory. More generally, the "linearity" of quantum mechanics is something which has nothing to do ..
Feb
15
comment The open problem of finding the explicit metric on a compact Calabi-Yau manifold
Maybe it is worth mentionning that some work has been done to approximate numerically Ricci flat metrics on compact Calabi-Yau manifolds: see for example arxiv.org/pdf/math/0512625v1.pdf and arxiv.org/pdf/hep-th/0612075.pdf The first paragraph of the second paper contains the phrase: "it is widely thought that for compact Calabi-Yau manifolds no closed form expression exists, except in trivial cases", which makes me pessimistic on the existence of a positive answer to the question.
Feb
15
comment “Arithmetic genus” of a plane curve singularity.
@Gregor Bruns : Thanks a lot. I have corrected the formula in the answer.
Feb
15
revised “Arithmetic genus” of a plane curve singularity.
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3
revised Lie algebra $\mathfrak{so}(9)$ as a subalgebra of $\mathfrak{f}_4$
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Jan
3
revised Why is the CM closure of $\mathbb{Q}$ the “ultimate” coefficient field for motives?
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