相关论文: Some remarks on Borel type ideals
Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…
The aim of this paper is to study the relationship between reduction numbers and Borel-fixed ideals in all characteristics. By definition, Borel-fixed ideals are closed under certain specializations which is similar to the strong stability.…
The number of ad-nilpotent ideals of the Borel subalgebra of the classical Lie algebra of type B_n is determined using combinatorial arguments involving a generalization of Dyck-paths. We also solve a similar problem for the untwisted…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and…
In this paper, we show that the regularity of the q-th quasi-symbolic power $I^{((q))}$ and the regularity of the $q$-th bracket power $I^{[q]}$ of a monomial ideal of Borel type $I$, satisfy the relations $reg(I^{((q))})\leq q \cdot…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
We extend the recent classification of Hilbert schemes with two Borel-fixed points to arbitrary characteristic. We accomplish this by synthesizing Reeves' algorithm for generating strongly stable ideals with the basic properties of…
We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non…
We estimate the Castelnuovo-Mumford regularity of ideals in a polynomial ring over a field by studying the regularity of certain modules generated in degree zero and with linear relations. In dimension one, this process gives a new type of…
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible…
We use the notion of Borel generators to give alternative methods for computing standard invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals. Because there are generally few Borel generators relative to…
We investigate the question whether a given homogeneous ideal is a limit of saturated ones. We provide cohomological necessary criteria for this to hold and apply them to a range of examples. Our motivation comes from the theory of border…
We prove that in normal rings the tight closure of an ideal can be computed as the sum of the ideal and a piece of the tight closure, called the special tight closure.
We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is…
We obtain some new inequalities of Chebyshev Type.
This paper proves that the Castelnuovo-Mumford regularities of the product and sum of two monomial complete intersection ideals are at most the sum of the regularities of the two ideals, and provides examples showing that these inequalities…
We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic…