Results 1 to 10 of about 294 (116)
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 ...
P -A Absil, Guillaume Olikier
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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
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Homological projective duality for determinantal varieties
Advances in Mathematics, 2016 23 pages.
Michele Bolognesi +2 more
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On the conormal bundle of the determinantal variety
Journal of Algebra, 1982 Call W such variety. If we choose bases B(V) = {a,,..., a,], B(U) = v i ,..., b,} for each module, we can identify W with the variety of pairs of matrices (Y, x) with entries in R, X being an m X n matrix, Y an II X m matrix, such that x. Y=Omx, Y.X=Onxm.
Elisabetta Strickland
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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
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Determinantal loci and the flag variety
Advances in Mathematics, 1989 The author asks for the connection between a recent generalization of the ``second fundamental theorem'' of invariant theory due to Abhyankar and the geometry of the flag variety \(FL(n)=\sqcup W(\tau) \), where the W(\(\tau)\) are the Bruhat cells of FL(n). The Zariski closure of a W(\(\tau)\) in FL(n) is called a Schubert variety X(\(\tau)\) in FL(n).
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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
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Determinacy of determinantal varieties [PDF]
manuscripta mathematica, 2018 10 ...
Imran Ahmed, Maria Aparecida Soares Ruas
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Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
Physical Review X, 2021 The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the
Alexander Wietek +4 more
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Tropical positivity and determinantal varieties
Algebraic Combinatorics, 2023 We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We focus on the study of low-rank matrices, in particular matrices of rank
Brandenburg, Marie Charlotte +2 more
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