Timeline for Can every Hodge structure be polarized?
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| Sep 10, 2020 at 22:44 | comment | added | AmorFati | Thanks for your answer. The equivalence between Hodge structures of type $\{ (1,0), (0,1) \}$ and complex tori is given as follows? Let $H_{\mathbb{Z}}$ be a lattice of rank $2n$ with $\phi : H_{\mathbb{Z}} \to H_{\mathbb{Z}}$ an endomorphism. Take the eigenvalues $\lambda_1, ..., \lambda_{2n}$ of $\phi$ to be distinct with non-zero imaginary part. Let $H^{1,0}$ be the eigenspace of $\lambda_1, ..., \lambda_n$, such that $\lambda_i \neq \overline{\lambda_j}$ for any $1 \leq j \leq n$. The torus is then $T = H/(H^{1,0} \oplus H_{\mathbb{Z}})$? | |
| Sep 8, 2020 at 22:01 | vote | accept | AmorFati | ||
| Sep 8, 2020 at 15:39 | history | edited | Donu Arapura | CC BY-SA 4.0 |
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| S Sep 8, 2020 at 14:59 | history | answered | Donu Arapura | CC BY-SA 4.0 | |
| S Sep 8, 2020 at 14:59 | history | made wiki | Post Made Community Wiki by Donu Arapura |