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For questions about Heegaard-Floer homology (as introduced by Ozsváth-Szabó in 2003) and its uses in 3- and 4-dimensional topology.

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Is $Sym^g$ of a Riemann Surface of genus $g$ Calabi-Yau?

This is not a Calabi-Yau if $g\ne 1$ (for any definition of Calabi-Yau). Indeed, there is a degree one map from the symmetric power of the curve to a torus of dimension $g$. Pull-back of the volume f …
Dmitri Panov's user avatar
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