Related papers: Uniqueness properties for spherical varieties
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomorphism. Moreover the former admit infinitely many…
We describe the generic singularity of a Schubert variety of type A on each irreducible component of its singular locus. This singularity is given either by a cone of rank one matrices, or a quadratic cone.
We invent the notion of a derived and fluid variety. Fluid variety has no proper derived variety as its subvariety. We examine some properties of fluid and derived varieties. Examples of such varieties of bands are presented.
In this paper we classify all the quivers and corresponding dimension vectors having a smooth space of semisimple representation classes. The result is that these quiver settings can be reduced via some specific reduction steps to 3 simple…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this fundamental theorem to fields of…
Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.
Using the higher analytic torsion form of Bismut and Lott we construct a characteristic class for smooth sphere bundles. We calculate this class in the case where the sphere bundle comes from a complex vector bundle. Related to these…
We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves.
Feature Selection techniques aim at finding a relevant subset of features that perform equally or better than the original set of features at explaining the behavior of data. Typically, features are extracted from feature ranking or subset…
We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal…
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in…
In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities.…
This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…