Related papers: Algebraic bounds on analytic multiplier ideals

We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of…

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur…

In modeling physical systems it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases,…

In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…

We prove an averaged version of a claim suspected to be true by Alladi, Erd\"os, and Vaaler. Qualitatively, the result states that a divisor sum of a multiplicative function, which obeys certain size constraints, derives most of its value…

We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit allowing us to treat…

The paper concerns nilpotent associative dialgebras and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five-term cohomological sequence under alternative conditions in…

In this paper, we will give an upper bound of the number of auxiliary hypersurfaces in the determinant method, which reformulates an unpublished work of Salberger by Arakelov geometry. One of the key constants will be determined by the…

This paper gives an explicit formula for the multiplier ideals, and consequently for the log canonical thresholds, of any GL(V)xGL(W)-invariant ideal in the symmetric algebra S of the tensor product of V with the dual of W, where V and W…

We present a generalization of the multiplier ideal version of inversion of adjunction, often known as the restriction theorem, to centers of arbitrary codimension. We approach inversion of adjunction from the subadjunction point of view.…

In this paper we define and explore the analytic spread $\ell(\mathcal I)$ of a filtration in a local ring. We show that, especially for divisorial and symbolic filtrations, some basic properties of the analytic spread of an ideal extend to…

For an effective divisor on a smooth algebraic variety or a complex manifold, we show that the associated multiplier ideals coincide essentially with the filtration induced by the filtration V constructed by B. Malgrange and M. Kashiwara.…

Let $C \geq 1$. Inspired by the LLL-algorithm, we define strongly $C$-reduced divisors of a number field $F$ which are generalized from the concept of reduced Arakelov divisors. Moreover, we prove that strongly $C$-reduced Arakelov divisors…

Potential theory on the complement of a subset of the real axis attracts a lot of attention both in function theory and applied sciences. The paper discusses one aspect of the theory - the logarithmic capacity of closed subsets of the real…

We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

Thompson (2014) exhibits a formula for the multiplier ideal with multiplier lambda of a monomial curve C with ideal I as an intersection of a term coming from the I-adic valuation, the multiplier ideal of the term ideal of I, and terms…

We prove a gluing theorem which allows to construct an ample divisor on a rational surface from two given ample divisors on simpler surfaces. This theorem combined with the Cremona action on the ample cone gives rise to an algorithm for…

We prove a refinement of Ado's theorem for Lie algebras over an algebraically-closed field of characteristic zero. We first define what it means for a Lie algebra $L$ to be approximated with a nilpotent ideal, and we then use such an…

Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $\phi:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of…