DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kwak, Si-Jong | - |
dc.contributor.advisor | 곽시종 | - |
dc.contributor.author | Song, Yeong-Seok | - |
dc.contributor.author | 송영석 | - |
dc.date.accessioned | 2011-12-14T04:40:55Z | - |
dc.date.available | 2011-12-14T04:40:55Z | - |
dc.date.issued | 2010 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=455383&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41944 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.08, [ iii, 40 p. ] | - |
dc.description.abstract | In this thesis, we study the degree complexity of an integral curve in $\mathbb{p^{3}}$ and a smooth surface in $\mathbb{p^{4}}$ with respect to the lexicographic order. Let $\It{I}$ be the defining ideal of an integral curve in $\mathbb{p^{3}}$ of degree d and arithmetic genus $\rho_{a}}. If we fix a term order as the lexicographic order. Then the degree complexity of $\It{I}$ in generic coordinates is $1+(\binom{d-1}{2})-\rho_{a}}$ with exception of two cases. Additionally if $S \subset\p^{4}$ is smooth surface cut out by quadric and $\It{I_S}$ is the defining ideal of $\It{S}$ then the degree complexity of $I_S$ in generic coordinates $\It{M(I_{S})}$ is $1+\binom{d_{1}-1}{2}-\rho_{a}(Y_{1})$, where $d_{1}=\deg(Y_{1}(S))=\binom{d-1}{2}-\rho_{a}(S \cap H)$ with exception of three cases. If $\It{S}$ is a rational normal scroll then $\It{M(I_{S})=3}$, if $\It{S}$ is a complete intersection of (2,2)-type then $\It{M(I_{S})=4}$, and if $\It{S}$ is a Castelnuovo surface then $\It{M(I_{S})=5}$. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 정칙성 | - |
dc.subject | 부분 소거 ideals | - |
dc.subject | Generic 초항 | - |
dc.subject | 그레브너 기저 | - |
dc.subject | Regularity | - |
dc.subject | Generic initial ideal | - |
dc.subject | Partial elimination ideals | - |
dc.subject | Grober basis | - |
dc.title | (The) degree complexity via Generic initial ideals and applications | - |
dc.title.alternative | Generic initial ideals 를 매개로한 복잡도와 응용 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 455383/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020035151 | - |
dc.contributor.localauthor | Kwak, Si-Jong | - |
dc.contributor.localauthor | 곽시종 | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.