Related papers: Star configurations in $\mathbb P^n$
In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $\mathbb{R}^n$ is introduced. We describe the structure of the semigroup $\mathbf{PStH}_{\mathbb{R}^n}$ of star partial homeomorphisms of the…
Published version: We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially $(\mathbb P^1)^n$. A combinatorial characterization, the $(\star)$-property, is known in $\mathbb…
The Jacobian ideal of a hyperplane arrangement is an ideal in the polynomial ring whose generators are the partial derivatives of the arrangements defining polynomial. In this article, we prove that an arrangement can be reconstructed from…
Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci-Harbourne defined a quantity called the resurgence to…
Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar…
In this paper we define some combinatorial principles to characterize spaces $X$ whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
We investigate the possibility of very early formation of primordial star clusters from high-\sigma perturbations in cold dark matter dominated structure formation scenarios. For this we have developed a powerful 2-level hierarchical…
We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are…
Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed…
Taking a novel approach, this paper discuss the structure of compact stars, an important topic in theoretical astrophysics. Adopting the Newtonian gravitation, we solve the hydrostatic equilibrium equation by imposing a simple…
We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on $\mathbb{C}^{(p+q)\cdot p~*}$, the space of $(p+q)\times p$ matrices of rank p, invariant under the right…
We will start from the beginning and define a matroid and its Orlik-Solomon algebra and holonomy Lie algebra, but first we give some background from topology and cohomology. A (central) hyperplane arrangement is a finite number of subspaces…
We study the structure of neutron stars in scalar-tensor theories for the nonminimal coupling of the form $(1+\kappa \xi \phi^{2})\cal R$. We solve the hydrostatic equilibrium equations for two different types of scalar field potentials and…
We consider current state of star formation theory and requirements to observations in millimeter and submillimeter ranges which are necessary for resolution of the most actual problems of the physics of star formation. Two key features of…
I review theoretical models of star formation and how they apply across the stellar mass spectrum. Several distinct theories are under active study for massive star formation, especially Turbulent Core Accretion, Competitive Accretion and…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…
A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…
Massive stars (~8-25Msun) stripped of their hydrogen-rich envelopes via binary interaction are thought to be the main progenitors for merging neutron stars and stripped-envelope supernovae. We recently presented the discovery of the first…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…