Related papers: Resolution except for minimal singularities II. Th…
We show that a positive proportion of linear forms in four variables admit a solution in the primes that is as small as one would heuristically expect. Out of the linear forms that satisfy certain local solvability conditions, almost all…
First, this paper presents a systematic procedure for constructing criteria for singularities of curves of finite multiplicities in $\boldsymbol{R}^N$. Based on this method, we provide explicit criteria for singularities of multiplicities…
Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these…
The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only…
We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a…
This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…
The topic of this paper is the Finiteness Conjecture for minimally unsatisfiable clause-sets (MUs), stating that for each fixed deficiency (number of clauses minus number of variables) there are only finitely many patterns, given a certain…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
This is the major revision. The main purpose of this paper is to prove that minimal discrepancies of $n$-dimensional toric singularities can accumulate only from above and only to minimal discrepancies of toric singularities of dimension…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free…
In this article, we prove the existence of at least two positive weak solutions for a mixed local-nonlocal singular problem in the presence of critical exponential nonlinearity in dimension two. The novelty of this work is the inclusion of…
Scalar curvature constraints can be studied by means of splitting procedures. The success of this strategy depends on the control we can get on its splitting factors. We introduce canonical so-called minimal splitting factors. They have…
It is a conjecture of Koll\'ar that a variety $X$ with rational singularities in some open subvariety $U$ has a rationalification; that is, a proper, birational morphism $f: Y \rightarrow X$ such that $Y$ has rational singularities, and…
Four-dimensional black hole solutions generated by the low energy string effective action are investigated outside and inside the event horizon. A restriction for a minimal black hole size is obtained in the frame of the model discussed.…
We show that a version of the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the…
In this paper, we investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form $\mathbb{C}^2/G$. We refer to these as "bamboo-type" singularities, since the dual graphs of…
The singular set of a viscosity solution to a Hamilton-Jacobi equation is known to propagate, from any noncritical singular point, along singular characteristics which are curves satisfying certain differential inclusions. In the…