相关论文: Toric Rigid Spaces

We provide a concise and accessible introduction to (geometric) string structures, highlighting their connection to loop spaces and outlining relationships with neighboring topics.

We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches…

We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings

We give a method to construct deep holes for elliptic curve codes. For long elliptic curve codes, we conjecture that our construction is complete in the sense that it gives all deep holes. Some evidence and heuristics on the completeness…

A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…

I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…

The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in the context of $4$-dimensional toric…

We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…

It is shown in this paper that it is possible, at least in principle, to construct a traversable wormhole that is stable to linearized radial perturbations by specifying relatively simple conditions on the shape and redshift functions.

We extend the formalism of "log spaces" of arXiv:1507.06752 to topoi equipped with a sheaf of monoids, and discuss Deligne--Faltings structures and root stacks in this context.

An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…

This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a…

We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.

In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…

In a previous paper, the author and David Swinarski constructed the moduli spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction which…

A toric variety is a normal complex variety which is completely described by combinatorial data, namely by a fan of strongly convex rational (with respect to a lattice) cones. Due to this rationality condition, toric varieties are…

We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…

In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…

We introduce a Zariskian analogue of the theory of Huber's adic spaces.