Components of the Hilbert scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components.

Autor: Choi, Youngook, Iliev, Hristo, Kim, Seonja
Zdroj: Manuscripta Mathematica; Nov2024, Vol. 175 Issue 3/4, p921-942, 22p
Abstrakt: Let I d , g , r be the union of irreducible components of the Hilbert scheme whose general points represent smooth, irreducible, non-degenerate curves of degree d and genus g in P r . Using a family of curves found on ruled surfaces over smooth curves of genus γ , we show that for γ ≥ 7 and g ≥ 6 γ + 5 , the scheme I 2 g - 4 γ + 1 , g , g - 3 γ + 1 acquires a non-reduced component D ′ such that dim T [ X ′ ] D ′ = dim D ′ + 1 for a general point [ X ′ ] ∈ D ′ . [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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