컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0325 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Algebraic Geometry (AL-3) |
| 영문제목 (Title(Eng.)) |
Asymptotic and finite Hilbert stability of algebraic varieties |
| 저자(Author(s)) |
Donghoon Hyeon1 Seoul National University1 |
| 초록본문(Abstract) | To polarize the Hilbert scheme, one should use the defining equations of high enough degree. Only then we are able to consider the Geometric Invariant Theory (GIT) stability of the Hilbert points of algebraic varieties, and this is called the asymptotic Hilbert stability. Asymptotic Hilbert stability has been used by David Gieseker in his GIT construction of the moduli space of stable curves. When we use equations of degree larger than or equal to the regularity, we can still define the Hilbert point although we may not be able to polarize the whole Hilbert scheme. In this talk, we shall explain how the GIT of Hilbert points of low degree (called the finite Hilbert stability) can be defined in a meaningful way, and how it can be applied to the study of the birational geometry of the moduli space of stable curves. |
| 분류기호 (MSC number(s)) |
14 |
| 키워드(Keyword(s)) | Geometric Invariant Theory |
| 강연 형태 (Language of Session (Talk)) |
English |