TY  - Type of reference 
TI  - From a defective Segre-Veronese embedding to a non-defective one adding a factor 
AU  - Edoardo Ballico 
AB  - Fix $$$x\in \mathbb{N}$$$, a multiprojective space $$$Y$$$ and a very ample line bundle $$$L$$$ on $$$Y$$$ . We say that $$$(Y,L)$$$ satisfies $$$\pm{x}\star$$$-non-defectivity if the $$$s$$$-secant variety of $$$(Y, L)$$$ has the expected dimension if either $$$(\dim Y+1)(s+x)\le h^0(L)$$$ or $$$(\dim Y +1)(s-x)\ge h^0(L)$$$. Natural examples arise when $$$L$$$ is the Segre line bundle and all factors have the same dimension (Abo - Ottaviani - Peterson). We take integers $$$r > 0$$$, $$$t\ge 2$$$ and set $$$X:= Y\times \mathbb{P}^r$$$. Let $$$L[t]$$$ be the line bundle on $$$X$$$ coming from $$$L$$$ and $$$\mathcal{O}_{\mathbb{P}^r}(t)$$$. 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 $$$r\le 2$$$. In particular we extend a recent result by Ballico, Bernardi and Mańduz on the non-defectivity of Segre-Veronese embeddings of multidegree $$$(t_1,\dots ,t_k)$$$ of $$$(\mathbb{P}^2)^k$$$, $$$k\ge 3$$$, to the case in which $$$t_i=1$$$ for $$$y > 0$$$ integers $$$i:$$$ we require $$$y\ge 9$$$. 
DO  - 10.21494/ISTE.OP.2025.1341 
JF  - Advances in Pure and Applied Mathematics 
KW  - Segre-Veronese variety, secant variety, partially symmetric tensors, secant defective variety, bounded defectivity, Segre-Veronese variety, secant variety, partially symmetric tensors, secant defective variety, bounded defectivity,  
L1  - https://www.openscience.fr/IMG/pdf/iste_apam25v16n4_2.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2025/09/4 
SN  - 1869-6090 
TT  - D’un plongement Segre-Veronese défectif à un autre non-défectif en ajoutant un facteur 
UR  - https://www.openscience.fr/From-a-defective-Segre-Veronese-embedding-to-a-non-defective-one-adding-a 
IS  - Issue 4 (September 2025) 
VL  - 16 
ER  -