In https://arxiv.org/pdf/1504.00690.pdf, it seems like the "derived manifold structure" given on a certain complex analytic space seems to have the real virtual dimension the same as the complex virtual dimension of the original (derived) scheme over $\mathbb{C}$. I have little knowledge in anything that's behind this, so what does this result really mean? Particularly, what does it mean for a derived manifold over a complex analytic space to have an odd real virtual dimension?
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