Related papers: Resolution of singularities of null cones
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
The article provides a local classification of singularities of meromorphic second order linear differential equation with respect to analytic/meromorphic linear point transformations. It also addresses the problem of determining the Lie…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We construct special conics configurations from some points configurations which are the singularities of the dual of a quartic curve.
The purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations in which the multiplicity of a hypersurface is a…
We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra \g and the resonance varieties R(V,K)\subset V^* attached to irreducible \g-modules V and submodules K\subset V\wedge V. In the…
We show Laplacian algebras are maximal, and give applications to the Classical Invariant Theory of real orthogonal representations of compact groups, including: The solution of the Inverse Invariant Theory problem for finite groups. An…
This paper presents a canonical dual approach for solving nonconvex quadratic minimization problem. By using the canonical duality theory, nonconvex primal minimization problems over n-dimensional Lorentz cone can be transformed into…
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of…
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
We begin with a short exposition of the theory of lattice varieties. This includes a description of their orbit structure and smooth locus. We construct a flat cover of the lattice variety and show that it is a complete intersection. We…
We show that the theories of some (ordered) central simple algebras with involution over real closed fields are model-complete or admit quantifier elimination, and characterize positive cones in terms of morphisms into models of some of…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
We study the "generic" degenerations of curves with two singular points when the points merge. First, the notion of generic degeneration is defined precisely. Then a method to classify the possible results of generic degenerations is…
Given a rational convex polyhedral Gorenstein cone constructed as cone over a lattice polytope P, we establish that toric non-commutative crepant resolutions (NCCRs) of its associated toric algebra descend to toric NCCRs of the algebras…
We derive explicit expressions of the homogeneous solutions in two dimensional cones for Pucci's extremal equations. As examples of possible applications, we obtain monotonicity formulas for all nonnegative supersolutions and necessary and…
We investigate sets of the common zeros of non-constant semi-invariants for regular modules over canonical algebras. In particular, we show that if the considered algebra is tame then for big enough vectors these sets are complete…
We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $ K_C $-orbits in the Lagrangian Grassmannian as the categorical…
We give a short proof that essentially all questions concerning singularities of Richardson varieties reduce to corresponding questions about Schubert varieties. Consequently, we quickly deduce some new and previously known results.
Each object of any abelian model category has a canonical resolution as described in this article. When the model structure is hereditary we show how morphism sets in the associated homotopy category may be realized as cohomology groups…