Some Fano manifolds whose Hilbert polynomial is totally reducible over $\mathbb Q$
| Autor: | Lanteri, Antonio, Tironi, Andrea Luigi |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $(X,L)$ be any Fano manifold polarized by a positive multiple of its fundamental divisor $H$. The polynomial defining the Hilbert curve of $(X,L)$ boils down to being the Hilbert polynomial of $(X,H)$, hence it is totally reducible over $\mathbb C$; moreover, some of the linear factors appearing in the factorization have rational coefficients, e.g. if $X$ has index $\geq 2$. It is natural to ask when the same happens for all linear factors. Here the total reducibility over $\mathbb Q$ of the Hilbert polynomial is investigated for three special kinds of Fano manifolds: Fano manifolds of large index, toric Fano manifolds of low dimension, and Fano bundles of low coindex. Comment: 19 pages |
| Databáze: | arXiv |
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