On some components of Hilbert schemes of curves

2021/01/24 by Flaminio Flamini, Flamini, Flaminio, Paola Supino +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2101.09684

Abstract

Let I_d,g,R be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree d, genus g, which are non--degenerate in the projective space ℙ^R. Under some numerical assumptions on d, g and R, we construct irreducible components of I_d,g,R other than the so-called \em distinguished component, dominating the moduli space M_g of smooth genus--g curves, which are generically smooth and turn out to be of dimension higher than the expected one. The general point of any such a component corresponds to a curve X ⊂ ℙ^R which is a suitable ramified m--cover of an irrational curve Y ⊂ ℙ^R-1, m \geqslant 2, lying in a surface cone over Y. The paper extends some of the results in previous papers of Y. Choi, H. Iliev, S. Kim (cf. [12,13] in Bibliography).

Citations

• On the projective normality of complete linear series on an algebraic curve

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