A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture
| Autor: | Choe, Junho, Kwak, Sijong |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $K_{p,1}$ 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. Comment: 40 pages, any comments are welcome, the abstract and introduction have been slightly revised, we also shortened the paper (now 40 pages, originally 53) |
| Databáze: | arXiv |
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