11 papers
Secant varieties of flag varieties via Schur apolarity
Alessandra Bernardi, Stefano Canino, Vincenzo Antonio Isoldi
We develop a general first-order theory of Schur apolarity for the study of secant varieties of flag varieties in arbitrary homogeneous embeddings. Extending the classical apolarit…
New conjectures on multiplicities of tensor eigenvalues
Stefano Canino, Cosimo Flavi, Francesco Galuppi +1
We work on two conjectures on tensor eigenvalue multiplicities. By using the language of algebraic geometry we give stronger, more refined versions of the conjectures and we prove…
A new bound on the rank of tensor product of W-states
S. Canino, A. Casarotti, P. Santarsiero
A W-state is an order d symmetric tensor of the form W_d=x^{d-1}y. We prove that the partially symmetric rank of W_{d_1}\otimes \cdots \otimes W_{d_k} is at most 2^{k-1}(d_1+\cdots…
Detecting Direct Sums of Tensors and Their Limits
S. Canino, C. Flavi, J. Jelisiejew
We generalize Mammana's classification of limits of direct sums to more than two factors. We also extend it from polynomials to arbitrary Segre-Veronese format, generalising and un…
Isotropic Rank of Harmonic Polynomials
S. Canino, C. Flavi
Any homogeneous harmonic polynomial can be decomposed as a sum of powers of isotropic linear forms, that is, linear forms whose coefficients are the coordinates of isotropic points…
Postulation of schemes of length at most 4 on surfaces
E. Ballico, S. Canino
In this paper we address the postulation problem of zero-dimensional schemes on a surface of length at most 4. We prove some general results and then we focus on the case of P2, P1…
Postulation for 2-superfat points in the plane
Stefano Canino, Maria Virginia Catalisano, Alessandro Gimigliano +2
We study the postulation of 0-dimensional schemes given by unions of 2-superfat points in general position in the plane, i.e., the union of local schemes defined by the intersectio…
Superfat points and associated tensors
Stefano Canino, Maria Virginia Catalisano, Alessandro Gimigliano +1
We consider 0-dimensional schemes supported at a single point in n-space that are m-symmetric, i.e. that intersect any smooth curve passing through the point with length m, and the…
On the Jacobian Scheme of a plane curve
Stefano Canino, Alessandro Gimigliano, Monica Idà
We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity, characterizing it through a geometric property. We compute the Tjurina number for a family of cu…
Newton-Puiseux algorithm and triple points for planes curves
Stefano Canino, Alessandro Gimigliano, Monica Idà
The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximat…
Complete intersections on Veronese surfaces
Stefano Canino, Enrico Carlini
In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection su…