Related papers: Logarithmically Regular Morphisms

We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

For a rank 1 local system on the complement of a reduced divisor on a complex manifold $X$, its cohomology is calculated by the twisted meromorphic de Rham complex. Assuming the divisor is everywhere positively weighted homogeneous, we…

Let $G$ be a connected reductive linear algebraic group. We consider the normal $G$-varieties with horospherical orbits. In this short note, we provide a criterion to determine whether these varieties have at most canonical, log canonical…

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

The logarithmic multiplicative group is a proper group object in logarithmic schemes, which morally compactifies the usual multiplicative group. We study the structure of the stacks of logarithmic maps from rational curves to this…

In this paper we continue our research line on logical characterizations of behavioral metrics obtained from the definition of a metric over the set of logical properties of interest. This time we provide a characterization of both strong…

We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine,…

We study Bloch-Ogus theory and the Gersten conjecture for homology theories with duality satisfying certain properties, in particular for \'etale cohomology with finite coefficients coprime to the residue characteristic of the base, for…

Motivated by a question of Hansen and Li, we show that a smooth and proper rigid analytic space $X$ with projective reduction satisfies Hodge symmetry in the following situations: (1) the base non-archimedean field $K$ is of residue…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

We construct a logarithmic model of connections on smooth quasi-projective $n$-dimensional geometrically irreducible varieties defined over an algebraically closed field of characteristic $0$. It consists of a good compactification of the…

We first study hyperplane sections of some singular schemes over a field. We prove a Bertini theorem for the log smoothness of generic hyperplane sections of a large class of log smooth schemes over a log point. We also give an abstract…

Let ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this paper is…

We introduce a logarithmic cobordism $\omega^{\text{Log}}$ ring of pairs $(X,D)$ of varieties equipped with a simple normal crossings divisor $D\subset X$, analogous to the algebraic cobordism ring $\omega^{\text{LP}}$ of…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…