The ideal of a Segre variety $\mathbb{P}^{n_{1}}\times \cdots \times\mathbb{P}^{n_{t}}\hookrightarrow \mathbb{P}^{(n_{1}+1)\cdots (n_{t}+1)-1}$ is generated by the $2$-minors of a generic hypermatrix of indeterminates. We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of ``weak generic hypermatrix'' which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension $2$.
Alessandra Bernardi (2008). Ideals of varieties parameterized by certain symmetric tensors. JOURNAL OF PURE AND APPLIED ALGEBRA, 212, 1542-1559 [10.1016/j.jpaa.2007.10.022].
Ideals of varieties parameterized by certain symmetric tensors
BERNARDI, ALESSANDRA
2008
Abstract
The ideal of a Segre variety $\mathbb{P}^{n_{1}}\times \cdots \times\mathbb{P}^{n_{t}}\hookrightarrow \mathbb{P}^{(n_{1}+1)\cdots (n_{t}+1)-1}$ is generated by the $2$-minors of a generic hypermatrix of indeterminates. We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of ``weak generic hypermatrix'' which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension $2$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
