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A curved Brunn--Minkowski inequality on the discrete hypercube
A curved Brunn--Minkowski inequality discrete hypercube
2010/11/24
We compare two approaches to Ricci curvature on non-smooth spaces, in the case of the discrete hypercube $\{0,1\}^N$. While the coarse Ricci curvature of the first author readily yields a positive va...
We use the CR geometry of the standard hyperquadric in complex projective three-space to give a detailed twistor description of conformal foliations in Euclidean three-space.
We study self-duality of Grothendieck's blended extensions (extensions panach\'ees) in the context of a tannakian category. The set of equivalence classes of symmetric, resp. antisymmetric, blended ex...
Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curva...
On the dual of the mobile cone
the mobile cone math
2010/11/24
We prove that the cone of mobile divisors and the cone of curves birationally movable in codimension $1$ are dual in the $(K+B)$-negative part for a klt pair $(X/Z,B)$. We also prove the structure th...
We give a necessary and sufficient condition in order for a hyperplane arrangement to be of Torelli type, namely that it is recovered as the set of unstable hyperplanes of its Dolgachev sheaf of loga...
Matrices with restricted entries and q-analogues of permutations
Matrices q-analogues of permutations
2010/11/23
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restrict...
Geometrization of principal series representations of GL_N associated to regular characters
Geometrization principal series representations
2010/11/23
In geometric representation theory, one often wishes to describe representations realized on spaces of invariant functions as trace functions of equivariant perverse sheaves. In the case of principal...
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenval...
McMullen's g-vector is important for simple convex polytopes. This paper postulates axioms for its extension to general convex polytopes. It also conjectures that, for each dimension d, a stated fini...
Group Width
Group Width Geometric Topology
2010/11/18
There are many "minimax" complexity functions in mathematics: width of a tree or a link, Heegaard genus of a 3-manifold, the Cheeger constant of a Riemannian manifold. We define such a function w, "wi...
Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category
2-dimensional quadrics geometry derived category
2010/11/23
Given a generic family $Q$ of 2-dimensional quadrics over a smooth 3-dimensional base $Y$ we consider the relative Fano scheme $M$ of lines of it. The scheme $M$ has a structure of a generically coni...
Shioda described in his article from 1986 a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over k(t)...
On the Seshadri constants of adjoint line bundles
the Seshadri constants adjoint line bundles
2010/11/9
In the present paper we are concerned with the possible values of Seshadri constants. While in general every positive rational number appears as the local Seshadri constant of some ample line bundle, ...
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions
Global well-posedness scattering the defocusing cubic NLS
2010/11/11
In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. ...