Related papers: Relative Resolution and Its Applications
The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an…
We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…
We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of…
The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…
We study the stable hom relation for Cohen-Macaulay modules over Gorenstein local algebras. We give the sufficient condition to make the stable hom relation a partial order when the base algebra is of finite representation type. As an…
We continue our study of relatively divisible and relatively flat objects in exact categories in the sense of Quillen with several applications to exact structures on finitely accessible additive categories and module categories. We derive…
In this paper, we will construct the injective resolution of any $\cR$-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in ($\cR$-2-Mod).
Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…
For the magnetic Hamiltonian with singular vector potentials, we analytically continue the resolvent to a logarithmic neighborhood of the positive real axis and prove resolvent estimates there. As applications, we obtain asymptotic…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps…
We work over an arbitrary ring R. Given two truncated projective resolutions of equal length for the same module we consider their underlying chain complexes. We show they may be stabilized by projective modules to obtain a pair of…
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…