컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0328 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Algebraic Geometry (AL-3) |
| 영문제목 (Title(Eng.)) |
Components rigid in moduli and the irreducibility of the Hilbert scheme of smooth projective curves |
| 저자(Author(s)) |
Changho Keem1 Seoul National University1 |
| 초록본문(Abstract) | Denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which 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 talk, we discuss about 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 discuss 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 $r$. These results are partly by products of the irreducibility of $\mathcal{H}_{d,g,3}$ beyond the range which has been known before. |
| 분류기호 (MSC number(s)) |
Primary 14H10; Secondary 14C05 |
| 키워드(Keyword(s)) | Hilbert scheme, algebraic curves, linear series, component rigid in moduli |
| 강연 형태 (Language of Session (Talk)) |
English |