(A) matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture고차 시컨트 다양체의 마트료시카 구조와 일반화된 브로노프스키 추측

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In this paper, we propose a matryoshka structure of higher secant varieties which includes many matryoshka phenomena in the category of higher secant varieties, and which generalizes certain celebrated classical results in the study of syzygy to higher secant varieties. For example, we prove a generalized $K_{p,1}$ theorem for higher secant varieties, the syzygetic and geometric characterizations of minimal degree higher secant varieties, defined by Ciliberto and Russo ([15]), and del Pezzo higher secant varieties, defined in this paper, and also give the determinantal presentation of higher secant varieties having minimal degree. These results come mainly from the structure of tangent cones to higher secant varieties and from inductive analyses of defining equations and their syzygies in relation to inner and tangential projections. For our purposes, we prove a weak form of the generalized Bronowski's conjecture due to Ciliberto and Russo ([15]) that relates the identifiability for higher secant varieties to the geometry of tangential projections.
Advisors
Kwak, Sijongresearcher곽시종researcher
Description
한국과학기술원 :수리과학과,
Country
한국과학기술원
Issue Date
2021
Identifier
325007
Language
eng
Article Type
Thesis(Ph.D)
URI
http://hdl.handle.net/10203/294688
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=962385&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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