Related papers: Inverting log blow-ups in log geometry

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically…

We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor computing the minimal log discrepancy computes no log…

We consider blow-up solutions of a semilinear wave equation with a loglog perturbation of the power nonlinearity in the subconformal case, and show that the blow-up rate is given by the solution of the associated ODE which has the same…

The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution process, both classical and modern. In this paper we explore how it changes by blowing--up.

We classify embedded blowups of the real affine plane up to oriented isomorphy. We show that two blowups in the same isomorphism class are isotopic, using a matrix deformation argument similar to an idea given by Shastri. This answers two…

The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is established. This result extends those of…

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.…

We show that 3-fold terminal flips and divisorial contractions to a curve may be factored by a sequence of weighted blow-ups, flops, blow-downs to a locally complete intersection curve in a smooth 3-fold or divisorial contractions to a…

We introduce the notion of log motivic triangulated categories, which is the theoretical framework for understanding the motivic aspect of cohomology theories for fs log schemes. Then we study the Grothendieck six operations formalism for…

We establish the motivic six-functor formalism for fs log schemes. In particular, we prove the exact base change property, projection formula, and Poincar\'e duality. We also define Borel-Moore motivic homology, G-theory, and Chow homology…

Let $H$ and $H'$ be two ample line bundles over a smooth projective surface $X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable (resp. $H'$-semistable) sheaves of fixed type $(r,c_1,c_2)$. We construct a sequence of…

We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smooth closed immersions in derived algebraic geometry.

Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten…

In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.

Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…

We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.

We provide a procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history,…

Let $S$ be a smooth projective surface, and $\hat{S}$ be its blow-up at a point. In this paper, we study the derived category of the Hilbert scheme of points on the blow-up $\hat{S}$. We obtain a semi-orthogonal decomposition consisting of…

We study the logarithmic vector bundles associated to arrangements of smooth irreducible curves with small degree on the blow-up of the projective plane at one point. We then investigate whether they are Torelli arrangements, that is, they…

We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral…