Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Turatti, Ettore Teixeira"'
Publikováno v:
Journal of Algebra, Volume 661, 1 January 2025, Pages 641-656
Let $f$ be a homogeneous polynomial of even degree $d$. We study the decompositions $f=\sum_{i=1}^r f_i^2$ where $\mathrm{deg} f_i=d/2$. The minimal number of summands $r$ is called the $2$-rank of $f$, so that the polynomials having $2$-rank equal t
Externí odkaz:
http://arxiv.org/abs/2402.05189
After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties. For del Pezzo surfaces, we give a full description of the Terracini loci. Moreover, we present an algorithm to explicitly co
Externí odkaz:
http://arxiv.org/abs/2311.09067
We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order $d \geq 3$ and dimension $2$ and symmetric tensors of order $3$ and dimension $3$, we prove that only finitely many tensors sha
Externí odkaz:
http://arxiv.org/abs/2308.10957
Subtracting a critical rank-one approximation from a matrix always results in a matrix with a lower rank. This is not true for tensors in general. Motivated by this, we ask the question: what is the closure of the set of those tensors for which subtr
Externí odkaz:
http://arxiv.org/abs/2303.14985
A singular $k$-tuple of a tensor $T$ of format $(n_1,\ldots,n_k)$ is essentially a complex critical point of the distance function from $T$ constrained to the cone of tensors of format $(n_1,\ldots,n_k)$ of rank at most one. A generic tensor has fini
Externí odkaz:
http://arxiv.org/abs/2206.08606
Publikováno v:
Journal of Pure and Applied Algebra, Volume 228, Number 7, 2024
We study the problem of how many different sums of squares decompositions a general polynomial $f$ with SOS-rank $k$ admits. We show that there is a link between the variety $\mathrm{SOS}_k(f)$ of all SOS-decompositions of $f$ and the orthogonal grou
Externí odkaz:
http://arxiv.org/abs/2206.07473
Publikováno v:
In Journal of Pure and Applied Algebra July 2024 228(7)
Autor:
Turatti, Ettore Teixeira
Publikováno v:
SIAM Journal on Applied Algebra and Geometry, Vol. 6 Iss. 2 (2022)
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some general tensor, which are all the tensors that admit those same singular tup
Externí odkaz:
http://arxiv.org/abs/2104.03686
We state the relation between the variety of binary forms of given rank and the dual of the multiple root loci. This is a new result for the suprageneric rank, as a continuation of the work by Buczy\'nski, Han, Mella and Teitler. We describe the stra
Externí odkaz:
http://arxiv.org/abs/2007.03335
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