arXiv subjects

C. Bocci

Publications and source records attributed to C. Bocci.

4 recordsLinked to original sources

arXiv2022

Hadamard products of symbolic powers and Hadamard fat grids

In this paper we address the question if, for points $P, Q \in \mathbb{P}^{2}$, $I(P)^{m} \star I(Q)^{n}=I(P \star Q)^{m+n-1}$ and we obtain different results according to the number of zero coordinates in $P$ and $Q$. Successively, we use our results to define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicities. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed.

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↗

arXiv2008

A tropical interpretation of m-dissimilarity maps

Let T be a weighted tree with n numbered leaves and let D be its distance matrix, so D(i,j) is the distance between the leaves i and j. If m is an integer between 2 and n, we prove a tropical formula to compute the m-dissimilarity map of T (i.e. the weights of the subtrees of T with m leaves), given D. For m equal to 3, we present a tropical description of the set of m-dissimilarity maps of trees. For m equal to 4, a partial result is given.

math.AG↗

arXiv2004

Osculating spaces to secant varieties

We generalize the classical Terracini's Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the $d$-Veronese embedding of the projective 3-space.

math.AG↗