Components of the Hilbert scheme of smooth projective curves using ruled surfaces
| Autor: | Seonja Kim, Hristo Iliev, Youngook Choi |
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| Rok vydání: | 2020 |
| Předmět: |
Degree (graph theory)
General Mathematics 010102 general mathematics Algebraic geometry 01 natural sciences Moduli space Combinatorics Number theory Hilbert scheme Scheme (mathematics) Genus (mathematics) 0103 physical sciences Component (group theory) 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | manuscripta mathematica. 164:395-408 |
| ISSN: | 1432-1785 0025-2611 |
| Popis: | Let $${\mathcal {I}}_{d,g,r}$$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree d and genus g in $$\mathbb {P}^r$$ . We use families of curves on cones to show that under certain numerical assumptions for d, g and r, the scheme $${\mathcal {I}}_{d,g,r}$$ acquires generically smooth components whose general points correspond to curves that are double covers of irrational curves. In particular, in the case $$\rho (d,g,r) := g-(r+1)(g-d+r) \ge 0$$ we construct explicitly a regular component that is different from the distinguished component of $${\mathcal {I}}_{d,g,r}$$ dominating the moduli space $${\mathcal {M}}_g$$ . Our result implies also that if $$g \ge 57$$ then $${\mathcal {I}}_{\frac{4g}{3}, g, \frac{g+1}{2}}$$ has at least two generically smooth components parametrizing linearly normal curves. |
| Databáze: | OpenAIRE |
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