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Article overview
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Irreducibility and components rigid in moduli of the Hilbert scheme of smooth curves | Changho Keem
; Yun-Hwan Kim
; Angelo Felice Lopez
; | Date: |
1 May 2016 | Abstract: | Denote by $mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, that is
the union of components whose general point corresponds to a smooth irreducible
and non-degenerate curve of degree $d$ and genus $g$ in $mathbb P^r$. A
component of $mathcal{H}_{d,g,r}$ is rigid in moduli if its image under the
natural map $pi:mathcal{H}_{d,g,r} dashrightarrow mathcal{M}_{g}$ is a one
point set. In this note, we provide a proof of the fact that
$mathcal{H}_{d,g,r}$ has no components rigid in moduli for $g > 0$ and $r=3$.
In case $r geq 4$, we also prove the non-existence of a component of
$mathcal{H}_{d,g,r}$ rigid in moduli in a certain restricted range of $d$,
$g>0$ and $r$. In the course of the proofs, we establish the irreducibility of
$mathcal{H}_{d,g,3}$ beyond the range which has been known before. | Source: | arXiv, 1605.0297 | Services: | Forum | Review | PDF | Favorites |
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