Related papers: Potential log canonical centers

Let $(X,\Delta)$ be a log canonical $4$-fold over an algebraically closed field of characteristic zero. We prove that any sequence of $(K_X+\Delta)$-flips terminates.

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

In this article we show that if $(X, \Delta)$ is a log canonical compact K\"ahler $3$-fold such that $K_X+\Delta$ is nef and the numerical dimension $\nu(K_X+\Delta)\neq 2$, then $K_X+\Delta$ is semi-ample.

We prove that for lambda = beta_omega or just lambda strong limit singular of cofinality aleph_0, if there is a universal member in the class K^lf_lambda of locally finite groups of cardinality lambda, then there is a canonical one…

Given a hypersurface defined by $f$ in a smooth complex algebraic variety $X$, and a point $P$ on this hypersurface, we consider the invariant $\beta_P(f)$ given by the log canonical threshold at $P$ of ${\mathfrak m}_P\cdot J_f$, where…

Rational pairs generalize the notion of rational singularities to reduced pairs $(X,D)$. In this paper we deal with the problem of determining whether a normal variety $X$ has a rationalizing divisor, i.e. a reduced divisor $D$ such that…

Given an ideal $\mathcal{I}$ on $\omega$, we prove that a sequence in a topological space $X$ is $\mathcal{I}$-convergent if and only if there exists a ``big'' $\mathcal{I}$-convergent subsequence. Then, we study several properties and show…

In this paper, we study the behavior of the sets of volumes of the form $\mathrm{vol}(X,K_X+B+M)$, where $(X,B)$ is a log canonical pair, and $M$ is a nef $\mathbb{R}$-divisor. After a first analysis of some general properties, we focus on…

We compute a canonical circular-arc representation for a given circular-arc (CA) graph which implies solving the isomorphism and recognition problem for this class. To accomplish this we split the class of CA graphs into uniform and…

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa's conjecture on exponential sums, with the log-canonical threshold in the…

We prove that a Kawamata log terminal pair has the canonical model.

Zeta generators are derivations associated with odd Riemann zeta values that act freely on the Lie algebra of the fundamental group of Riemann surfaces with marked points. The genus-zero incarnation of zeta generators are Ihara derivations…

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

For indefinite (Pontryagin space) canonical systems that contain an inner singularity we prove the existence of generalised boundary values at the singularity, which are used to formulate interface conditions. With the help of such…

We show that the log canonical threshold of a generic determinantal variety and its generic link are the same.

We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.

We show that log canonical thresholds satisfy the ACC

Given a Schubert variety X_w, we exhibit a divisor \Delta, defined over the integers, such that the pair (X_w,\Delta) is log Fano in all characteristics.

We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$. Both examples…