Related papers: Integral morphisms and log blow-ups
The purpose of this paper is to describe several applications of finiteness properties of $F$-finite $F$-modules recently discovered by M. Hochster to the study of Frobenius maps on injective hulls, Frobenius near-splittings and to the…
We define the Frobenius morphism of certain class of noncommutative blowups in positive characteristic. Thanks to a nice property of the class, the defined morphism is flat. Therefore we say that the noncommutative blowups in this class are…
A semialgebraic map $f:X\to Y$ between two real algebraic sets is called blow-Nash if it can be made Nash (i.e. semialgebraic and real analytic) by composing with finitely many blowings-up with non-singular centers. We prove that if a…
In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent…
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling…
In this article, we analyze the connection between the Log De Rham Cohomology of an fs (not necessary log smooth) log scheme $Y$ over $\mathbb C$ (for $Y$ admitting an exact closed immersion into an fs log smooth log scheme over $\mathbb…
We generalize the Cartier transform of Ogus and Vologodsky to log smooth schemes. More precisely, we generalize a local version of this transform, due to Shiho, and a topos-theoretic version, due to Oyama. Let $k$ be a perfect field of…
This paper is concerned with a multi-component Camassa-Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa-Holm type systems as special cases. In…
Fulton and MacPherson famously constructed a configuration space that encodes infinitesimal collision data by blowing up the diagonals. We observe that when generalizing their approach to configuration spaces of filtered manifolds (e.g. jet…
Blowing up a point p in a manifold M builds a new manifold M' in which p is replaced by the projectivization of the tangent space of M at p. This well-known operation also applies to fixed points of diffeomorphisms, yielding continuous…
The integrality of Ooguri-Vafa disk invariants is verified using discrete symmetries of the superpotential of the mirror Landau-Ginzburg theory to calculate quantum corrections to the boundary variables. We show that these quantum…
Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
We prove the decomposition theorem for Hodge modules with integral structure along proper K\"ahler morphisms, partially generalizing M. Saito's theorem for projective morphisms. Our proof relies on compactifications of period maps of…
We call a local homeomorphism $f: (R^n,0)\to(R^n,0)$ blow-analytic if it becomes real analytic after composing with a finite number blowings-up with smooth nowhere dense centers. If the graph of $f$ is semi-algebraic then, by a theorem of…
We extend the construction of A$_{\rm inf}$-cohomology by Bhatt-Morrow-Scholze to the context of log $p$-adic formal schemes over a log perfectoid base. In particular, using coordinates, we prove comparison theorems between log A$_{\rm…
In this paper we apply Shokurov's inductive method to study terminal and canonical singularities. As an easy consequence of the Minimal Model Program we show that for any three-dimensional log terminal singularity there exists some special,…
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 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.…
This paper demonstrates the existence of $\mathbb{Q}$-complements for algebraically integrable log-Fano foliations on klt ambient varieties. Additionally, we investigate properties of algebraically integrable Fano foliations such as a…
This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of…