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Geometry of moduli space of stable maps and degeneration
스테이블 사상의 모듈라이 공간의 기하와 변형

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Authors
노현호
Advisor
조철현
Major
자연과학대학 수리과학부
Issue Date
2015-08
Publisher
서울대학교 대학원
Keywords
stable maps
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 조철현.
Abstract
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.
Language
English
URI
https://hdl.handle.net/10371/121298
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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