Related papers: Blow-ups of canonical singularities

We analyse a blow-up sequence of solutions for Liouville type equations involving Dirac measures with "collapsing" poles. We consider the case where blow-up occurs exactly at a point where the poles coalesce. After proving that a…

Categorical resolution of singularities has been constructed in arXiv:1212.6170. It proceeds by alternating two steps of seemingly different nature. We show how to use the formalism of filtered derived categories to combine the two steps…

We prove that, for the jet scheme of a singular hypersurface, the blowup of a certain jet-related module is not an isomorphism. In conjunction with recent developments in the theory of Nash blowups, our result holds over fields of arbitrary…

We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space $\mathbb{R}^2$ and on the upper half-plane $\mathbb{R}^2_+$, allowing infinite energy. In each case, we…

We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be $C^{1}$ at…

We study the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), a mass-critical and completely integrable dispersive model. Recent works established finite-time blow-up constructions and soliton resolution, describing…

We show that iterating Nash blowups resolve the singularities of normal toric surfaces satisfying the following property: the minimal generating set of the corresponding semigroup is contained in one or two segments. We also provide…

In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface \Sigma. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang and we extend it to the case of…

We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical…

The first examples of exceptional terminal singularities are constructed.

We introduce a straightforward method to analyze the blow-up of systems of ordinary differential inequalities, and apply it to study the blow- up of solutions to a weakly coupled system of semilinear heat equations. We prove that the…

We extend the formula for the Chern classes of blow-ups of algebraic varieties due to Porteous and Lascu-Scott, and of symplectic and complex manifolds due to Geiges and Pasquotto, to the blow-ups of almost complex manifolds. Our approach…

We consider the energy critical four dimensional semi linear heat equation \partial tu-\Deltau-u3 = 0. We show the existence of type II finite time blow up solutions and give a sharp description of the corresponding singularity formation.…

We study the formation of generic singularities of mean curvature flow by combining the different approaches, specifically the methods in studying blowup of nonlinear heat equations, the techniques used by the author and the collaborators…

Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical…

We initiate the study of Nash blowups in prime characteristic. First, we show that a normal variety is non-singular if and only if its Nash blowup is an isomorphism, extending a theorem by A. Nobile. We also study higher Nash blowups, as…

Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk…

We study the blowup algebras of the modules that are direct sums of ideals generated by either maximal minors of a ladder matrix or unit interval determinantal ideals. Specifically, we determine Gr\"{o}bner bases for the presentation ideals…

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then…

We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile.