A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture

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In projective algebraic geometry, there are classical and fundamental results that describe the structure of geometry and syzygies, and many of them characterize varieties of minimal degree and del Pezzo varieties. In this paper, we consider analogous objects in the category of higher secant varieties. Our main theorems say that there is a matryoshka structure among those basic objects including a generalized Kp,1 theorem, syzygetic and geometric characterizations of higher secant varieties of minimal degree and del Pezzo higher secant varieties, defined in this paper. For our purpose, we prove a weak form of the generalized Bronowski's conjecture raised by C. Ciliberto and F. Russo that relates the identifiability for higher secant varieties to the geometry of tangential projections. (C) 2022 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2022-09
Language
English
Article Type
Article
Citation

ADVANCES IN MATHEMATICS, v.406, pp.1 - 9

ISSN
0001-8708
DOI
10.1016/j.aim.2022.108526
URI
http://hdl.handle.net/10203/297663
Appears in Collection
MA-Journal Papers(저널논문)
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