Related papers: Minimal model program for semi-stable threefolds i…

We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

We establish Maxwell compactness results for the Discrete De Rham (DDR) polytopal complex: sequences in this polytopal complex with bounded discrete $\boldsymbol{H}(\mathbf{curl})$ (resp. discrete $\boldsymbol{H}(\mathrm{div})$) norm and…

Let $(X, \Delta)$ be a projective klt three dimensional pair defined over an algebraically closed field characteristic larger than 5. Let $L$ be a nef and big line bundle on $X$ such that $L-K_X-\Delta$ is big and nef. We show that $L$ is…

We consider a class of stable smoothable n-dimensional varieties, the analogs of stable curves. Assuming the minimal model program in dimension n+1, we prove that this class is bounded. From Kollar's method of constructing projective moduli…

We shall prove that any small deformation of a Q-factorial projective symplectic variety with terminal singularities is locally rigid; in other words, it preserves the singularity. In particular, many singular symplectic moduli of…

We define combinatorial analogues of stable and unstable minimal surfaces in the setting of weighted pseudomanifolds. We prove that, under mild conditions, such combinatorial minimal surfaces always exist. We use a technique, adapted from…

We discuss the minimal model program for projective morphisms of complex analytic spaces. Roughly speaking, we show that the results obtained by Birkar--Cascini--Hacon--M\textsuperscript{c}Kernan hold true for projective morphisms between…

In this paper, we explore the geometry of potential triples $(X,\Delta,D)$, which by definition consists of a pair $(X,\Delta)$ and an $\mathbb{R}$-Cartier pseudoeffective divisor $D$ on $X$. We define and study the asymptotic multiplier…

In 2007 Kawamata proved that two different minimal models can be connected by a sequence of flops. The aim of this paper is to show that the same holds true for 2 foliated minimal models descending from a common 3-fold pair equipped with a…

It was shown that in robustly transitive, partially hyperbolic diffeomorphisms on three dimensional closed manifolds, the strong stable or unstable foliation is minimal. In this article, we prove ``almost all'' leaves of both stable and…

We show the termination of any log-minimal model program for a pair $(X,\Delta)$ of a symplectic manifold $X$ and an effective $\mathbb R$-divisor $\Delta$.

We develop the theory of $N$-mixed-spin-$P$ fields for Fermat-type hypersurfaces in $\mathbb{P}(1,1,1,1,2)$, $\mathbb{P}(1,1,1,1,4)$, and $\mathbb{P}(1,1,1,1,4)$, following the theory developed in arXiv:1809.08806 for the quintic threefold.

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…

We describe the recently established minimal model program for (non-algebraic) K\"ahler threefolds as well as the abundance theorem for these spaces.

A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…

We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and…

In 3-dimensional manifolds, we prove that generically in$Diff^1_m(M)$, the existence of a minimal expanding invariant foliation implies stable Bernoulliness.

An important local vanishing theorem for the minimal model program is the fact that klt singularities in characteristic zero are Cohen-Macaulay. In contrast, even in the narrow setting of terminal singularities of dimension 3, we show that…

Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic automorphism. It is shown that while…

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result…