Year: 2025
Type: article
Abstract: Fix x ∈ N, a multiprojective space Y and a very ample line bundle L on Y .We say that (Y, L) satisfies ±x -non-defectivity if the s-secant variety of (Y, L) has the expected dimension if eitherNatural examples arise when L is the Segre line bundle and all factors have the same dimension (Abo -Ottaviani -Peterson).We take integers r > 0, t ≥ 2 and set X := Y × P r .Let L[t] be the line bundle on X coming from L and O P r (t).Under certain assumptions on x, dim Y , h 0 (L), r and t we prove that L[t] is not secant defective.Two of the main results are for r ≤ 2. In particular we extend a recent result by Ballico, Bernardi and Ma ńduz on the non-defectivity of Segre-Veronese embeddings of multidegree (t 1 , . . ., t k ) of (P 2 ) k , k ≥ 3, to the case in which t i = 1 for y > 0 integers i: we require y ≥ 9.
Author: Edoardo Ballico
Institution: University of Trento
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413985823