相关论文: The set of toric minimal log discrepancies

We prove that for each positive integer $n$ there exists a positive number $\epsilon_n$ so that $n$-dimensional toric quotient singularities satisfy the ACC for mld's on the interval $(0,\epsilon_n)$. In the course of the proof, we will…

Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint arXiv:math.AG/0306221. That is, they focus on the fact that toric…

We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on…

We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating and a minimal generating set for G_2-invariants of several…

We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable…

In this note we explore how standard statistical distances are equivalent for discrete log-concave distributions. Distances include total variation distance, Wasserstein distance, and $f$-divergences.

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference…

In this paper we will introduce a certain type of morphisms of log schemes (in the sense of Fontaine, Illusie, and Kato) and investigate their moduli. Then by applying this we define a notion of toric algebraic stacks over arbitrary…

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.

A formula is derived for the log quantile difference of the temporal aggregation of some types of stable moving average processes, MA(q). The shape of the log quantile difference as a function of the aggregation level is examined and shown…

We discuss conditions for complete intersections in a toric variety which allow to compute Hodge numbers if the complete intersection is a quasi-smooth complete variety. A preliminary step is the computation of the Euler characteristic of…

In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…

Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…

As is well known, the "usual discrepancy" is defined for a normal Q-Gorenstein variety. By using this discrepancy we can define a canonical singularity and a log canonical singularity. In the same way, by using a new notion, Mather-Jacobian…

We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…

We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients.…

In topological data analysis persistence modules are used to distinguish the legitimate topological features of a finite data set from noise. Interleavings between persistence modules feature prominantly in the analysis. One can show that…

Log-periodic amplitudes appear in the critical behavior of a large class of systems, in particular when a discrete scale invariance is present. Here we show how to compute these critical amplitudes perturbatively when they originate from a…

By means of filters, minimal R_1 and minimal regular topologies are characterized on suitable intervals consisting of non-trivial R_0 topologies.

These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any…