Related papers: Symbolic powers of planar point configurations
A boundary behavior of mappings, which are closely related with Sobolev and Orlicz--Sobolev classes in the plane and in the space, is investigated. There are obtained theorems on boundary behavior of classes mentioned above.
We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset.
The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…
Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly…
We study the limit and initial behavior of the numerical function $f(k)=\depth S/I^k$. General properties of this function together with concrete examples arising from combinatorics are discussed.
We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In…
We show that the $p$-part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of $p$-power order. As a corollary we deduce that the set of zeros of prime power order…
We study higher jumping numbers and generalized test ideals associated to determinantal ideals over a field of positive characteristic. We work in positive characteristic and give a complete characterization of both families for ideals…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
In this survey article we give a brief history of symbolic powers and its connection with the interesting problem of set-theoretic complete intersection. We also state a few problems and conjectures. Recently, in connection to symbolic…
We completely determine the depth and regularity of symbolic powers of the fiber product of two homogeneous ideals in disjoint sets of variables, given knowledge of the symbolic powers of each factor. Generalizing previous joint work with…
This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The…
We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets…
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an…
We introduce the class of sparse symmetric shifted monomial ideals. These ideals have linear quotients and their Betti numbers are computed. Using this, we prove that the symbolic powers of the generalized star configuration ideal are…
Symmetric powers of quasi-projective schemes can be extended, in terms of left Kan extensions, to geometric symmetric powers of motivic spaces. In this paper, we study geometric symmetric powers and compare with various symmetric powers in…