Abstract
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety X. The case we concentrate on is when X is a Veronese variety, a Grassmannian or a Segre variety. Not only these varieties are among the ones that have been most classically studied, but a strong motivation in taking them into consideration is the fact that they parameterize, respectively, symmetric, skew-symmetric and general tensors, which are decomposable, and their secant varieties give a stratification of tensors via tensor rank. We collect here most of the known results and the open problems on this fascinating subject.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference227 articles.
1. Algebraic Geometry, A First Course;Harris,1992
2. Sulle varietà algebriche per le quali sono di dimensione minore dell’ ordinario, senza riempire lo spazio ambiente, una o alcuna delle varietà formate da spazi seganti;Palatini;Atti Accad. Torino Cl. Sci. Mat. Fis. Nat.,1909
3. Sulle vk per cui la varietÀ degli sh (h + 1) seganti ha dimensione minore delĽordinario
4. Sulla rappresentazione delle forme quaternarie mediante somme di potenze di forme lineari;Terracini;Atti della Reale Accademia delle Scienze di Torino,1916
5. Sopra la teoria delle figure polari delle curve piane del 4.o ordine
Cited by
21 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献