85 citations · 366 across the 53 of their papers we have counts for
52 papers · 1 filter
Geproci sets on skew lines in with two transversals
Luca Chiantini, Pietro De Poi, Lucja Farnik +6
The purpose of this work is to pursue classification of geproci sets. Specifically we classify -geproci sets which consist of points on each of skew lines, assumin…
Combinatorics of skew lines in with an application to algebraic geometry
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
This article introduces a previously unrecognized combinatorial structure underlying configurations of skew lines in , and reveals its deep and surprising connection…
Terracini loci of curves
Edoardo Ballico, Luca Chiantini
We study subsets S of curves X whose double structure does not impose independent conditions to a linear series L, but there are divisors D in |L| singular at all points of S. Thes…
On the classification of certain geproci sets
Luca Chiantini, Lucja Farnik, Giuseppe Favacchio +4
In this short note we develop new methods toward the ultimate goal of classifying geproci sets in . We apply these methods to show that among sets of points distr…
Decompositions and Terracini loci of cubic forms of low rank
Luca Chiantini, Fulvio Gesmundo
We study Waring rank decompositions for cubic forms of rank in variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition…
Configurations of points in projective space and their projections
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
We call a set of points an -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point …
On the study of decompositions of forms in four variables
Luca Chiantini
In the space of sextic forms in 4 variables with a decomposition of length 18 we determine and describe a closed subvariety which contains all non-identifiable sextics. The descrip…
On the description of identifiable quartics
Elena Angelini, Luca Chiantini
In this paper we study the identifiability of specific forms (symmetric tensors), with the target of extending recent methods for the case of variables to more general cases. I…
A footnote to a footnote to a paper of B. Segre
Luca Chiantini, Giorgio Ottaviani
The paper is devoted to a detailed study of sextics in three variables having a decomposition as a sum of nine powers of linear forms. This is the unique case of a Veronese image o…
On the Terracini locus of projective varieties
Edoardo Ballico, Luca Chiantini
We introduce and study properties of the Terracini locus of projective varieties X, which is the locus of finite subsets S of X such that 2S fails to impose independent conditions…
On secant defective varieties, in particular of dimension 4
Luca Chiantini, Ciro Ciliberto, Francesco Russo
In this paper we prove some general results on secant defective varieties. Then we focus on the 4--dimensional case and we give the full classification of secant defective 4--folds…
Minimality and uniqueness for decompositions of specific ternary forms
Elena Angelini, Luca Chiantini
The paper deals with the computation of the rank and the identifiability of a specific ternary form. Often, one knows some short Waring decomposition of a given form, and the probl…
Catalecticant intersections and confinement of decompositions of forms
Elena Angelini, Cristiano Bocci, Luca Chiantini
We introduce the notion of confinement of decompositions for forms or vector of forms. The confinement, when it holds, lowers the number of parameters that one needs to consider, i…
Sets of points which project to complete intersections
Luca Chiantini, Juan Migliore
The motivating problem addressed by this paper is to describe those non-degenerate sets of points in whose general projection to a general plane is a complete int…
On the identifiability of ternary forms
Elena Angelini, Luca Chiantini
We describe a new method to determine the minimality and identifiability of a Waring decomposition of a specific form (symmetric tensor) in three variables. Our method, whi…
Identifiability for a class of symmetric tensors
Elena Angelini, Luca Chiantini, Andrea Mazzon
We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree…
Hilbert functions and tensor analysis
Luca Chiantini
We show how well known tools of algebraic geometry for the study of finite sets can be fruitfully applied to the study of Waring decompositions of symmetric tensors (forms). We mai…
Identifiability beyond Kruskal's bound for symmetric tensors of degree 4
Elena Angelini, Luca Chiantini, Nick Vannieuwenhoven
We show how methods of algebraic geometry can produce criteria for the identifiability of specific tensors that reach beyond the range of applicability of the celebrated Kruskal cr…
Polynomials and the exponent of matrix multiplication
Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer +2
We define tensors, corresponding to cubic polynomials, which have the same exponent as the matrix multiplication tensor. In particular, we study the symmetrized matrix multipli…
On the dimension of contact loci and the identifiability of tensors
Edoardo Ballico, Alessandra Bernardi, Luca Chiantini
Let be an integral and non-degenerate variety. Set . We prove that if the -secant variety of has (the expected) dimension $(k+n-1…
Bounds on the tensor rank
Edoardo Ballico, Alessandra Bernardi, Luca Chiantini +1
We give a sufficient criterion for a lower bound of the cactus rank of a tensor. Then we refine that criterion in order to be able to give an explicit sufficient condition for a no…
Effective criteria for specific identifiability of tensors and forms
Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven
In applications where the tensor rank decomposition arises, one often relies on its identifiability properties for interpreting the individual rank- terms appearing in the decom…
Real identifiability vs complex identifiability
Elena Angelini, Cristiano Bocci, Luca Chiantini
Let be a real tensor of (real) rank . is 'identifiable' when it has a unique decomposition in terms of rank tensors. There are cases in which the identifiability fai…
Waring-like decompositions of polynomials - 1
Maria Virginia Catalisano, Luca Chiantini, Anthony V. Geramita +1
Let be a homogeneous form of degree in variables. A Waring decomposition of is a way to express as a sum of powers of linear forms. In this paper we co…