컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0621 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Algebraic geometry / Complex geometry (SS-04) |
| 영문제목 (Title(Eng.)) |
On projective curves of maximal regularity |
| 저자(Author(s)) |
Wanseok Lee1, Euisung Park2, Kiryoung Chung1 KIAS1, Korea University2 |
| 초록본문(Abstract) | Let $C \subset \P^r$ $(r\geq 3)$ be a nondegenerate irreducible projective curve of degree $d$ defined over an algebraically closed field of arbitrary characteristic. By a well-known result of Gruson-Lazarsfeld-Peskine, the Castelnuovo-Mumford regularity ${\rm reg}(C)$ of $C$ is bounded by ${\rm reg}(C) \leq d-r+2$. They further classified the extremal curves which fail to be $(d-r+1)$-regular, showing in particular that if $d \geq r+2$ then $C$ is a smooth rational curve with a unique $(d-r+2)$-secant line. In this talk, we study the problem to classify the curves of maximal regularity (i.e., ${\rm reg}(C) = d-r+2$), up to projective equivalence. |
| 분류기호 (MSC number(s)) |
14N05 |
| 키워드(Keyword(s)) | Castelnuovo-Mumford regularity, extremal secant line, projective equivalence, Hilbert scheme |
| 강연 형태 (Language of Session (Talk)) |
English |