Related papers: Pull-back of quasi-log structures

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus-Kov\'acs conjecture…

We prove that a projective semistable morphism of fs log analytic spaces yields polarized log Hodge structures in the canonical way.

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log…

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…

In our series of papers, we prove that smooth Fano threefolds in positive characteristic lift to the ring of Witt vectors. Moreover, we show that they satisfy Akizuki-Nakano vanishing, $E_1$-degeneration of the Hodge to de Rham spectral…

The present paper studies the structure of characteristic varieties of fundamental groups of graph manifolds. As a consequence, a simple proof of Papadima's question is provided on the characterization of algebraic links that have…

We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F:f(\Omega)\to \mathcal A_d(\mathbb R^n)$ of a quasiregular map $f:\Omega\to \mathbb R^n$ of finite degree $d$. We then develop a pull-back theory of…

We prove that the cohomology jump loci in the space of rank one local systems over a smooth quasi-projective variety are finite unions of torsion translates of subtori. The main ingredients are a recent result of Dimca-Papadima, some…

We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic…

We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and $\Theta$-reductivity of the moduli of K-semistable log…

We prove a generalization of the Fujita-Kawamata-Zuo semi-positivity Theorem for filtered regular meromorphic Higgs bundles and tame harmonic bundles. Our approach gives a new proof in the cases already considered by these authors. We give…

The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by…

By making use of Halperin's local systems over simplicial sets and the model structure of the category of diffeological spaces due to Kihara, we introduce a framework of rational homotopy theory for such smooth spaces with arbitrary…

We prove the following theorem characterizing Du Bois singularities. Suppose that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $\pi : \tld Y \to Y$ be a log resolution of $X$ in $Y$ that is an isomorphism outside of $X$. If…

For a log Fano manifold (X, D) with D\neq 0 and with the log Fano pseudoindex \geq 2, we prove that the restriction homomorphism Pic(X)\to Pic(D_1) of Picard groups is injective for any irreducible component D_1\subset D.The strategy of our…

We construct a log algebraic version of the homotopy sequence for a quasi-projective normal crossing log variety over a log point of characteristic zero and prove some exactness properties of it. Our proofs are purely algebraic.

In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric…

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using…

By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.

We construct a projective K-moduli space of quasimaps with a certain log Fano condition, which is regarded as a rational map from $\mathbb{P}^1$ to a projective space. Moreover, we investigate relationships between the K-moduli of quasimaps…