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Equivariant sheaves on $\mathbb P^1$

Let me explain why the line bundle $\mathcal{O}(1)$ does not admit a $\mathrm{PGL}(2)$-equivariant structure. …
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4 votes

What does the Serre functor of equivariant category of fractional CY category look like?

In the particular example that you mention, the Serre functor is given by tensor product with $\omega_E[1]$, where $\omega_E$ is the canonical line bundle with its natural equivariant structure. … Since $E$ is an elliptic curve, the underlying line bundle is trivial, so the only question is whether the equivariant structure is trivial or not. …
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