Results 1 to 10 of about 175 (164)
The Representation Type of Determinantal Varieties [PDF]
Algebras and Representation Theory, 2017 This is a postprint (AAM) of an article published in Algebras and Representation Theory.
Rosa Maria Miró-Roig, Miró-Roig Rosa M
exaly +5 more sources
Toric double determinantal varieties [PDF]
Communications in Algebra, 2021 Undergraduate ...
Patricia Klein
exaly +3 more sources
Geometric rank and linear determinantal varieties
European Journal of Mathematics, 2023 There are close relations between tripartite tensors with bounded geometric ranks and linear determinantal varieties with bounded codimensions. We study linear determinantal varieties with bounded codimensions, and prove upper bounds of the dimensions of the ambient spaces.
Runshi Geng
exaly +3 more sources
Linear codes associated to determinantal varieties
Discrete Mathematics, 2015 We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The case of varieties defined by the vanishing of 2 x 2 minors is considered in some detail.
Sudhir R Ghorpade +2 more
exaly +4 more sources
Mixed Ladder Determinantal Varieties
Journal of Algebra, 2000 The authors generalize the notion of ladder determinantal varieties, which was introduced by Abhyankar, by allowing ideals of minors of different size of a matrix of indeterminates. Then they explore the relation between these mixed ladder determinantal varieties and Schubert varieties. Next they show that, up to product by affine spaces, each of these
Gonciulea, Nicolae, Miller, Claudia
exaly +3 more sources
Homological projective duality for determinantal varieties
Advances in Mathematics, 2016 23 pages.
Michele Bolognesi +2 more
exaly +6 more sources
Chern classes and characteristic cycles of determinantal varieties
Journal of Algebra, 2018 Let $K$ be an algebraically closed field of characteristic $0$. For $m\geq n$, we define $τ_{m,n,k}$ to be the set of $m\times n$ matrices over $K$ with kernel dimension $\geq k$. This is a projective subvariety of $\bbP^{mn-1}$, and is called the (generic) determinantal variety.
Xiping Zhang
exaly +4 more sources
The irreducibility of ladder determinantal varieties
Journal of Algebra, 1986 Let \({\mathfrak R}=(X_{ij})_{1\leq i\leq \mu,1\leq j\leq \nu}\) be a matrix of indeterminates over a domain k, where \(\mu,\nu\in {\mathbb{N}}\). Let \(p\in {\mathbb{N}}\) with \(1\leq p\leq \min (\mu,\nu)\). A subset \({\mathfrak L}\) of \({\mathfrak R}\) is called a ladder if whenever \(X_{ij},X_{k\ell}\in {\mathfrak L ...
exaly +3 more sources
The minimality of determinantal varieties [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2020 Abstract The determinantal variety Σ p q
Bordemann, Martin +2 more
openaire +3 more sources
On the Continuity of the Tangent Cone to the Determinantal Variety [PDF]
Set-Valued and Variational Analysis, 2022 Tangent and normal cones play an important role in constrained optimization to describe admissible search directions and, in particular, to formulate optimality conditions. They notably appear in various recent algorithms for both smooth and nonsmooth low-rank optimization where the feasible set is the set $\mathbb{R}_{\leq r}^{m \times n}$ of all $m ...
Guillaume Olikier, P.-A. Absil
openaire +2 more sources