Related papers: Grassmann defectivity \`a la Terracini
We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
Secant defectivity of projective varieties is classically approached via dimensions of linear systems with multiple base points in general position. The latter can be studied via degenerations. We exploit a technique that allows some of the…
The ABCT variety $V(3,n)$ is the image closure of the rational Veronese map from the Grassmannian $\operatorname{Gr}(2,n)$ to the Grassmannian $\operatorname{Gr}(3,n)$. It was studied by Arkani-Hamed--Bourjaily--Cachazo--Trnka in the…
We introduce and study on examples a notion of the Artin shape for a motive related to a projective homogenous variety. We apply it to the problem of finding the complete motivic decomposition of the variety. Our examples cover unitary…
Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the…
Kamke \cite{Kamke1921} solved an analog of Waring's problem with $n$th powers replaced by integer-valued polynomials. Larsen and Nguyen \cite{LN2019} explored the view of algebraic groups as a natural setting for Waring's problem. This…
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…
This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…
In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…
In this paper we discuss the consistency concept of Williams coherence for imprecise conditional previsions, presenting a variant of this notion, which we call W-coherence. It is shown that W-coherence ensures important consistency…
Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…
In this paper we adress the question of I. Smirnov and K. Tucker on the dual $F$-signature of the Veronese subrings of polynomial rings in $n$ variables using methods of commutative algebra.
The Las Vergnas polynomial is an extension of the Tutte polynomial to cellularly embedded graphs. It was introduced by Michel Las Vergnas in 1978 as special case of his Tutte polynomial of a morphism of matroids. While the general Tutte…
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional…
Karonski, Luczak, and Thomason (2004) conjectured that, for any connected graph G on at least three vertices, there exists an edge weighting from {1,2,3} such that adjacent vertices receive different sums of incident edge weights.…
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored…
This is a survey article on Morse theory based on lectures to graduate students and advanced undergraduates. After a brief review of standard material, mostly without proofs, the Morse theory of complex Grassmannian manifolds is worked out…
We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…