Let S_h be the even pure spinors variety of a complex vector space V of even dimension 2h endowed with a non degenerate quadratic form Q and let σ_k(S_h) be the k-secant variety of S_h. We decribe a probabilistic algorithm which computes the complex dimension of σ_k (S_h). Then, by using an inductive argument, we get our main result: σ_3 (S_h) has the expected dimension except when h ∈ {7, 8}. Also we provide theoretical arguments which prove that S_7 has a defective 3-secant variety and S_8 has defective 3-secant and 4-secant varieties.
Higher Secants of Spinor Varieties
ANGELINI, Elena
2011
Abstract
Let S_h be the even pure spinors variety of a complex vector space V of even dimension 2h endowed with a non degenerate quadratic form Q and let σ_k(S_h) be the k-secant variety of S_h. We decribe a probabilistic algorithm which computes the complex dimension of σ_k (S_h). Then, by using an inductive argument, we get our main result: σ_3 (S_h) has the expected dimension except when h ∈ {7, 8}. Also we provide theoretical arguments which prove that S_7 has a defective 3-secant variety and S_8 has defective 3-secant and 4-secant varieties.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
