Data di Pubblicazione:
2023
Citazione:
Some Fano manifolds whose Hilbert polynomial is totally reducible over ℚ / A. Lanteri, A. Luigi Tironi. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 34:08(2023), pp. 2350040.1-2350040.23. [10.1142/S0129167X23500404]
Abstract:
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) reduces to the Hilbert polynomial of (X, H), hence it is totally reducible over C; moreover, some of the linear factors appearing in the factorization have rational coefficients, e.g. if X has index >= 2. It is natural to ask when the same happens for all linear factors. Here the total reducibility over 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 projectivized Fano bundles of low coindex.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Polarized manifold; Hilbert polynomial; Fano manifold; toric Fano manifold; Fano bundle
Elenco autori:
A. Lanteri, A. Luigi Tironi
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