Related papers: Closed points on schemes
We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
We classify minimal-degree curves in the Hilbert schemes of points on algebraic surfaces. When the algebraic surface is the projective plane, the nef cone and a flip structure of these Hilbert schemes are determined.
In this paper we determine the scheme-theoretic fixed points of pinned reductive group schemes acted upon by a group of pinning-preserving automorphisms. The results are used in a companion paper to establish a ramified geometric Satake…
Both the USA TST 2008 and the ELMO Shortlist 2013 suggested two issues that are connected to fixed points. These problems provide a strong linkage between the various attributes of specific points in a triangle. In this article, we will…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.
The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…
We present some recent results in Fibrewise General Topology with special regard to the theory of Tychonoff compactifications of mappings. Several open problems are also proposed.
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.