# Tag Info

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### Volume of the unitary group

As indicated by Igor Rivin, the volume of the unitary group is given by $vol(U(N))=(2\pi)^{(N^2+N)/2}/\prod_{k=1}^{N-1} k!$. The denominator is the Barnes G-function, which is well-known : http://...
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• 93.8k

### Axiomatic characterization of virtual fundamental classes?

Question 1 (compare virtual fundamental cycles of different perfect obstruction theories on space underlying space): There is essentially no relation between $[X]_\varphi$ and $[X]_{\varphi'}$ for ...
• 17.5k
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### Prerequisites for reading papers of arithmetic such as Ribet, Mazur, Faltings, Wiles

I don't know what you mean by Modular forms of moduli stack, I think maybe you mean modular forms on moduli stacks. Either way, you should probably have a look at the book by Katz--Mazur titled "...
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Let $K$ be a connected compact Lie group. The moduli space of flat $K$-bundles over an $n$-torus is homeomorphic to the character variety $Hom(\mathbb{Z}^n,K)/K$. The identity component of this ...