Related papers: On the containment hierarchy for simplicial ideals
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…
The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a…
In this paper, the containment problem for the defining ideal of a special type of zero dimensional subschemes of $\mathbb{P}^2$, so called quasi star configurations, is investigated. Some sharp bounds for the resurgence of these types of…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
A notion of sectional regularity for a homogeneous ideal $I$, which measures the regularity of its generic sections with respect to linear spaces of various dimensions, is introduced. It is related to axial constants defined as the…
We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This…
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…
We show how to lift any monomial ideal J in n variables to a saturated ideal I of the same codimension in n+t variables. We show that I has the same graded Betti numbers as J and we show how to obtain the matrices for the resolution of I.…
This paper opens the series of articles supplemental to the series (hep-th/9405050,q-alg/9610026,q-alg/9611003,q-alg/9611019,funct-an/9611003), which also lies in lines of general ideology exposed in the review (mp_arc/96-477). The main…
Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity element. This particular article focuses on an examination of…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
We study gravitationally bound, spherically symmetric equilibrium configurations consisting of ordinary (neutron-star) matter and of a phantom/ghost scalar field which provides the nontrivial topology in the system. For such mixed…
This paper presents a formulation of the notion of monotonicity on homogeneous spaces. We review the general theory of invariant cone fields on homogeneous spaces and provide a list of examples involving spaces that arise in applications in…
In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around…