지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
논문 기본 정보
- 자료유형
- 학위논문
- 저자정보
- 발행연도
- 2015
- 저작권
- 서울대학교 논문은 저작권에 의해 보호받습니다.
이용수0
이 논문의 연구 히스토리 (2)
- 이 논문의 후속연구가 궁금하신가요?
- 연관 학술논문 또는 학술발표를 통해 보다 발전된 연구결과를 확인하실 수 있습니다.
- 이 논문의 연구 히스토리 확인하기
초록· 키워드
오류제보하기
We study geometry of moduli space of holomorphic maps from curves to projective scheme through various compactifications. Most famous one is moduli
space of stable maps introduced by Kontsevich. When genus is one and target space is projective space, main component of moduli space of stable maps is nonsingular. Vakil and Zinger found some desingularization via modular blow ups. Kim introduced log stable maps with target expansions which gives another desingularization of moduli space of stable maps. We compare theses two desingularization. Also, Gross-Seibert and Abramovich-Chen defined logarithmic stable maps without target expansions. Using these moduli space, one can define log Gromov-Witten invariants. We prove the degeneration formula of log Gromov-Witten invariants.
space of stable maps introduced by Kontsevich. When genus is one and target space is projective space, main component of moduli space of stable maps is nonsingular. Vakil and Zinger found some desingularization via modular blow ups. Kim introduced log stable maps with target expansions which gives another desingularization of moduli space of stable maps. We compare theses two desingularization. Also, Gross-Seibert and Abramovich-Chen defined logarithmic stable maps without target expansions. Using these moduli space, one can define log Gromov-Witten invariants. We prove the degeneration formula of log Gromov-Witten invariants.
목차
ContentsAbstract i1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Comparison of two desingularizations of moduli space of stable maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 An example of degeneration . . . . . . . . . . . . . . . . . 102.4 The description of fiber in the moduli space of elliptic admissible stable maps . . . . . . . . . . . . . . . . . . . . . . . 122.5 The case of the degree 2 . . . . . . . . . . . . . . . . . . . 172.6 The case of the degree 3 . . . . . . . . . . . . . . . .. . . . 193 Degeneration of log stable maps . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Basic/Minimal stable log maps . . . . . . . . . . . . . . . 293.3 Simple degenerations . . . . . . . . . . . . . . . . . . . . . . 413.4 Proof of Theorem 3.1.1 . . . . . . . . . . . . . .. . . . . . . . 50Abstract (in Korean) iAcknowledgement (in Korean) ii
최근 본 자료
댓글(0)
0