S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Geometry of moduli space of stable maps and degeneration
스테이블 사상의 모듈라이 공간의 기하와 변형
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- stable maps
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 조철현.
- 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.