Related papers: ACC for local volumes
Let us consider subcritical Bernoulli percolation on a connected, transitive, infinite and locally finite graph. In this paper, we propose a new (and short) proof of the exponential decay property for the volume of clusters. We do not rely…
We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.
The Local Converse Problem is to determine how the family of the local gamma factors $\gamma(s,\pi\times\tau,\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi$ of $\mathrm{GL}_n(F)$, with…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
We consider pairs (X,A), where X is a variety with klt singularities and A is a formal product of ideals on X with exponents in a fixed set that satisfies the Descending Chain Condition. We also assume that X has (formally) bounded…
We generalize the rationality theorem of the accumulation points of log canonical thresholds which was proved by Hacon, M\textsuperscript{c}Kernan, and Xu. Further, we apply the rationality to the ACC problem on the minimal log…
We make some improvements to our previous results. First, we prove a version of our volume growth theorem which does not require any assumption on the first Betti number. Second, we show that our local regularity theorem only requires a…
In this note, using methods introduced by Hacon, McKernan and Xu, we study the accumulation points of volumes of varieties of log general type. First, we show that, if the set of boundary coefficients $\Lambda$ is DCC, closed under limits…
In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of…
The classical double bubble theorem characterizes the minimizing partitions of $\mathbb{R}^n$ into three chambers, two of which have prescribed finite volume. In this paper we prove a variant of the double bubble theorem in which two of the…
Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain condition. We show that any accumulation point of volumes of log canonical surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the volume of a log…
We show that log canonical thresholds for complex analytic spaces satisfy the ACC.
We give a new proof of the known Shunkov's Theorem on locally finite groups with the minimal condition for nonabelian subgroups and also an extension of the known Suchkova-Shunkov Theorem on Shunkov groups with the minimal condition for…
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
In this paper we present a new correlation inequality and use it for proving an Almost Sure Local Limit Theorem for the so-called Dickman distribution. Several related results are also proved
In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov…
We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms…
We show that generalized log canonical thresholds for complex analytic spaces satisfy the ACC and we characterize the accumulation points.
In this paper we study singularities in arbitrary characteristic. We propose Finite Determination Conjecture for Mather-Jacobian minimal log discrepancies in terms of jet schemes of a singularity. The conjecture is equivalent to the…
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.