Related papers: Equimultiple locus of embedded algebroid surfaces …

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…

We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces…

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…

Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required…

Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result…

We study F-blowups of non-F-regular normal surface singularities. Especially the cases of rational double points and simple elliptic singularities are treated in detail.

Consider the equivariant wave map equation from Minkowski space to a rotationnally symmetric manifold which has an equator (example: the sphere). In dimension 3, this article gives a necessary and sufficient condition for the existence of a…

This paper is concerned with finite blow-up solutions of a one dimensional complex-valued semilinear heat equation. We provide locations and the number of blow-up points from the viewpoint of zeros of the solution.

We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the…

We consider the problem of finding an ideal whose blowup defines the Nash blowup of a toric surface and such that its zero locus coincides with the singular set of the toric surface.

Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and…

We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka.…

Let X be a compact toric surface. There exists a sequence of torus equivariant blow-ups of X such that the blown-up toric surface obtained admits a cscK metric.

We compute the Nash blow-up of a cominuscule Schubert variety. In particular, we show that the Nash blow-up is algebraically isomorphic to another Schubert variety of the same Lie type. As a consequence, we give a new characterization of…

We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, we describe the relation between special Ulrich bundles on…

We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of…

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition.…

In this paper, we introduce polytopal $k$-wedge construction and blowdown of a simple polytope and inspect the effect on the retraction sequence of a simple polytope due to $k$-wedge construction and blowdown. In relation to this…

We construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…

This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution…