Timeline for On the dimension of the cohomology of toric manifolds
Current License: CC BY-SA 4.0
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| Sep 18, 2018 at 14:14 | comment | added | BrianT | Thanks for your comment @Sasha. However, I'm looking for a proof using properties of the ideals $I$ and $J$. Let me explain why: I'll use the notation $u = (u_1,...,u_n)$. My question comes from the fact that, I'm trying to understand why a certain other quotient is finite dimensional, mainly $$\mathbb{C}[u] \ / \ (I + J_r \cap \mathbb{C}[u]),$$ where $J_r$ is the submodule in $\mathbb{C}[u,u^{-1}]$ generated by monomials $u^m$ for which $m \in \mathbb{Z}^k$ and $p(m) \geq r$. | |
| Sep 17, 2018 at 19:18 | comment | added | Sasha | The singular cohomology of any smooth projective variety (not necessarily toric) is finite-dimensional. The explicit formula for the cohomology ring is not needed here. | |
| Sep 17, 2018 at 18:17 | history | asked | BrianT | CC BY-SA 4.0 |