Tropical Linear Spaces
- 주제어 (키워드) Gröbner basis , tropical basis , tropical variety , tropical linear space , matroid
- 발행기관 서강대학교 일반대학원
- 지도교수 박진형
- 발행년도 2022
- 학위수여년월 2022. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제 URI http://www.dcollection.net/handler/sogang/000000066543
- UCI I804:11029-000000066543
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권 보호를 받습니다.
초록 (요약문)
Tropical geometry can be thought of as the algebraic geometry over the tropical semiring. A tropical varieties is obtained by the tropicalization of an algebraic variety in algebraic torus, and it is a union of finitely many tropical hypersurfaces. In this thesis, we give a brief survey of basic properties of tropical varieties. Especially, we review Gröbner bases and tropical bases of ideals in Laurent polynomial rings for the construction of tropical varieties, and we state the fundamental theorem and the structure theorem of tropical geometry. Next, we study tropical linear spaces, which may be different from the tropicalizations of linear varieties in algebraic torus.We also give a combinatorial description of some tropical Grassmannians.
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