Related papers: Desingularization by blowings-up avoiding simple n…

We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current…

Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions…

We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This extends the results from Bartolucci-Jevnikar-Lee-Yang…

We present a hypersurface singularity in positive characteristic which is defined by a purely inseparable power series, and a sequence of point blowups so that, after applying the blowups to the singularity, the same type of singularity…

We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up…

Let $X$ be any variety in characteristic zero. Let $V \subset X$ be an open subset that has toroidal singularities. We show the existence of a canonical desingularization of $X$ except for V. It is a morphism $f: Y \to X$ , which does not…

This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is our proposed globalization of a derived algebraic context,…

Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology…

Using Frobenius morphisms of noncommutative blowups, we prove that every normal toric singularity has a standard noncommutative resolution.

We generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field. The normal crossings condition considered by Goward is weakened to the condition that…

We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are…

We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…

We present a mesh refinement algorithm for detecting singularities of time-dependent partial differential equations. The main idea behind the algorithm is to treat the occurrence of singularities of time-dependent partial differential…

When considering a real log canonical threshold (RLCT) that gives a Bayesian generalization error, in general, papers replace a mean error function with a relatively simple polynomial whose RLCT corresponds to that of the mean error…

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…

In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

The only non-compact linearly stable singularity models for mean curvature flow are cylindrical by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on the cylinders has been established by the same authors. In this…