A study on some infinitely generated graded modules, projections, and applications = 무한 생성자를 갖는 차수 붙은 모듈과 사영사상 및 응용에 관한 연구

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We are interested in the algebraic and geometric structures of inner projections, partial elimination ideals and geometric applications. By developing the graded mapping cone construction and using the induced multiplicative maps on some infinitely generated graded modules, we obtain some (algebraic and geometric) properties of inner projections. As a result, for a projective reduced scheme $\It{X}$ of codimension e in $\mathbb{P}^{n}$ satisfying property $N_{2,p}$, $p\ge1$, we show that the inner projection from any smooth point of $\It{X}$ satisfies at least property $N_{2,p-1}$. Further, we obtain the main theorem on `embedded linear syzygies` which is the natural projection-analogue of `restricting linear syzygies` in the linear section case ([13]). This uniform behavior looks unusual in a sense that linear syzygies of outer projections heavily depend on moving the center of projection in an ambient space ([10],[25],[28]). Moreover, this property has many interesting corollaries such as ``rigidity theorem`` on property $N_{2,p}$, $e-1\le p \le e$ and the sharp lower bound $e \cdot p - \frac{p(p-1)}{2}$ of the number of quadrics vanishing on X satisfying property $N_{2,p},~ p \ge 1$. We also investigate the depth and Castelnuovo higher normality of inner projections which give useful information on the Betti diagram and the regularity conjecture due to Eisenbud-Goto and multisecants.
Advisors
Kwak, Sijongresearcher곽시종researcher
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
418794/325007  / 020045295
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.2, [ iv, 57 p. ]

Keywords

정칙성; 부분 소거 아이디얼; 사영사상; 매핑콘; 시지지; regularity; partial elimination ideal; mapping cone; projection; syzygy

URI
http://hdl.handle.net/10203/41936
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=418794&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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