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A. Lorenzini

Publications and source records attributed to A. Lorenzini.

3 recordsLinked to original sources
arXiv2019

On the Hadamard product of degenerate subvarieties

We consider generic degenerate subvarieties $X_i\subset\mathbb{P}^n$. We determine an integer $N$, depending on the varieties, and for $n\geq N$ we compute dimension and degree formulas for the Hadamard product of the varieties $X_i$. Moreover, if the varieties $X_i$ are smooth, their Hadamard product is smooth too. For $n<N$, if the $X_i$ are generically $d_i$-parameterized, the dimension and degree formulas still hold. However, the Hadamard product can be singular and we give a lower bound for the dimension of the singular locus.

math.AG↗
arXiv2016

On Hadamard products of linear varieties

In this paper we address the Hadamard product of linear varieties not necessarily in general position. In $\mathbb{P}^2$ we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets X and X' of collinear points, we get conditions for their hadamard product to be either a collinear finite set of points or a grid of | X|| X'| points. In $\mathbb{P}^3,$ under suitable conditions (which we prove to be generic), we show that the hadamard product of X and X' consists of | X||X'| points on the two different rulings of a non-degenerate quadric and we compute its Hilbert function in the case |X| = |X'|.

math.AG↗