Related papers: Potentially non-klt locus and its applications

The anticanonical complex has been introduced as a natural generalization of the toric Fano polytope and so far has been succesfully used for the study of varieties with a torus action of complexity one. In the present article we enlarge…

In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over R, and we carried out a detailed analysis of these objects on…

Let $\overline{\mathrm{Mov}}^k(X)$ be the closure of the cone $\mathrm{Mov}^k(X)$ generated by classes of effective divisors on a projective variety $X$ with stable base locus of codimension at least $k+1$. We propose a generalized version…

One of the central aims of the Minimal Model Program is to show that a projective log canonical pair $(X,\Delta)$ with $K_X+\Delta$ pseudoeffective has a good model, i.e.\ a minimal model $(Y,\Delta_Y)$ such that $K_Y+\Delta_Y$ is…

Let $f:(X,B)\to Z$ be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $p>5$, such that the coefficients of $\{B\}$ are in the standard set $\{1-\frac 1n|n\in \mathbb N\}$, then the…

We discuss in this note which K3 surfaces appear as anticanonical divisors in a Fano threefold. We prove in particular that a general K3 surface with given Picard lattice P and polarization class h in P is an anticanonical divisor in a Fano…

We prove that smooth non-klt toric orbifolds are separably Campana rationally connected, extending the result in the klt case. We also show that there always exists a positive characteristic in which a singular weighted projective space,…

Let $(X,\Delta)$ be a projective, $\mathbb{Q}$-factorial log canonical pair and let $L$ be a pseudoeffective $\mathbb{Q}$-divisor on $X$ such that $K_X + \Delta + L$ is pseudoeffective. Is there an effective $\mathbb{Q}$-divisor $M$ on $X$…

We introduce the notion of cracked polytope, and - making use of joint work with Coates and Kasprzyk - construct the associated toric variety $X$ as a subvariety of a non-singular toric variety $Y$ under certain conditions. Restricting to…

In this paper we develop non-stationary martingale techniques for dependent data. We shall stress the non-stationary version of the projective Maxwell-Woodroofe condition, which will be essential for obtaining maximal inequalities and…

A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial…

We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano…

We show that the anti-canonical volume of an $n$-dimensional K\"ahler-Einstein $\mathbb{Q}$-Fano variety is bounded from above by certain invariants of the local singularities, namely $\mathrm{lct}^n\cdot\mathrm{mult}$ for ideals and the…

In this paper we address Fano foliations on complex projective varieties. These are foliations whose anti-canonical class is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex…

We show that klt Fano varieties and certain lc Fano varieties contain free higher-genus curves in their smooth loci. Our methods also allow us to find free curves on varieties in positive characteristic and on quasiprojective varieties,…

We study K-stability properties of a smooth Fano variety X using non-Archimedean geometry, specifically the Berkovich analytification of X with respect to the trivial absolute value on the ground field. More precisely, we view…

Let $f:X\to U$ be a projective morphism of normal varieties and $(X,\Delta)$ a dlt pair. We prove that if there is an open set $U^0\subset U$, such that $(X,\Delta)\times_U U^0$ has a good minimal model over $U^0$ and the images of all the…

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…

Let $(X, \Delta)/U$ be klt pairs and $Q$ be a convex set of divisors. Assuming that the relative Kodaira dimensions are non-negative, then there are only finitely many log canonical models when the boundary divisors varying in a relatively…

In this paper we compute Lawson homology groups and semi-topological K-theory for some threefolds and fourfolds. We consider smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected…