Lower semi-continuity of waldschmidt constants = 발드슈미트 상수의 하반연속성

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Waldschmidt constants have been studied in different fields of mathematics, e.g., complex analysis, algebraic geometry, number theory and commutative algebra. After Nagata's work for the 14th Hilbert problem, these constants received great attention. In particular, in algebraic geometry, they recently have been rediscoverd by Bocci and Harbourne in the set-up of the containment relations between symbolic and ordinary powers of homogeneous ideals. In this paper, we study the Waldschmidt constant of a generalized fat point subscheme on the projective plane, which consists of essentially distinct points. Furthermore, we study various properties of the Waldschmidt constant of a generalized fat point subscheme which are related to complete ideal sheaves. Using these properties, we prove the lower semi-continuity of the Waldschmidt constants of generalized fat point subschemes which consists of less than or equal to 8 points. As an application, we also calculate the Waldschmidt constants of the generalized fat point subschemes which give rise to weak del Pezzo surfaces of degree 4.
Advisors
Lee, Yongnamresearcher이용남researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2019
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2019.2,[iii, 37 p. :]

Keywords

Waldschmidt constant▼afat point subscheme▼asymbolic power▼aweak del Pezzo surface▼aeffective cone; 발드슈미트 상수▼a두꺼운 점 도식▼a기호 거듭제곱▼a약 델 페조 곡면▼a유효원뿔

URI
http://hdl.handle.net/10203/264943
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=842148&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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