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Results tagged with ag.algebraic-geometry
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user 30909
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
The Hochschild cohomology of a variety "with coefficient" in a vector bundle
By adjunction $Rp_{1*}\mathcal{RHom}^*(\Delta_*E,\Delta_*E)=\mathcal{RHom}^*(\Delta^*\Delta_*E,E)$. By the splitting, you obtain $\mathcal{RHom}^*(\Delta^*\Delta_*E,E)=\mathcal{RHom}^*(E\otimes \Delta …
- 213
1
vote
Sheaf cohomology and double covers
Hints: I would show that $R^i\pi_*O_X=0$ for $i>0$, and then I would use adjunction.
(2) holds in general. Basically, you need to show that $\Gamma(Y,A\oplus B)=\Gamma(Y,A)\oplus \Gamma(Y,B)$.
- 213