Related papers: On the duality of moduli in arbitrary codimension
We find upper bounds for the essential dimension of various moduli stacks of $\sln$-bundles over a curve. When $n$ is a prime power, our calculation computes the essential dimension of the stack of stable bundles exactly and the essential…
We study the properties of the maximal volume $k$-dimensional sections of the $n$-dimensional cube $[-1,1]^n$. We obtain a first order necessary condition for a $k$-dimensional subspace to be a local maximizer of the volume of such…
In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz…
We study properties of graded maximal Cohen-Macaulay modules over an N-graded locally finite, Auslander Gorenstein, and Cohen-Macaulay algebra of dimension two. As a consequence, we extend a part of McKay correspondence in dimension two to…
We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…
The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded $k$-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several…
We prove that a bounded open set U in Euclidean n-space has k-width less than C(n) Volume(U)^{k/n}. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in Euclidean space. In particular, we…
The aim of this note is to find upper bounds on the dimension of Brill-Noether locus' inside the moduli space of rank two vector bundles on a smooth algebraic curve. We deduce some consequences of these bounds.
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of…
We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering…
We study the field of moduli of singular abelian and K3 surfaces. We discuss both the field of moduli over the CM field and over $\Q$. We also discuss non-finiteness with respect to the degree of the field of moduli. Finally, we provide an…
We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
Our goal is twofold. On one hand we show that the cones of divisors ample in codimension $k$ on a Mori dream space are rational polyhedral. On the other hand we study the duality between such cones and the cones of $k$-moving curves by…
We establish Euclidean-type lower bounds for the codimension-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in…
We answer a 15-year-old open question about the exact upper bound for bivariate copulas with a given diagonal section by giving an explicit formula for this bound. As an application, we determine the maximal asymmetry of bivariate copulas…
The object of this note is the moduli spaces of cubic fourfolds (resp., Gushel-Mukai fourfolds) which contain some special rational surfaces. Under some hypotheses on the families of such surfaces, we develop a general method to show the…
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…
The Euclidean operator radius of two bounded linear operators in the Hilbert $C^*$-module over $\A$ is given some precise bounds. Their relationship to recent findings in the literature that offer precise upper and lower bounds on the…