Related papers: On modules over valuations
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We discuss some relations of moduli of sheaves on rational surfaces by using universal extensions. These are a generalization of Maruyama's method to construct Uhlenbeck compactification of moduli of vector bundles.
The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced…
Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…
We introduce a theory of modules over a representation of a small category taking values in entwining structures over a semiperfect coalgebra. This takes forward the aim of developing categories of entwined modules to the same extent as…
The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and injective dimension, respectively. For a local ring $R$ and…
We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…
We construct the full linearisation functor which takes a graded bundle of degree $k$ (a particular kind of graded manifold) and produces a $k$-fold vector bundle. We fully characterise the image of the full linearisation functor and show…
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…
For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…
Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…
Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…
This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.
Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…
We study the motive of the moduli spaces of semistable rank two vector bundles over an algebraic curve. When the degree is odd the moduli space is a smooth projective variety, we obtain the absolute Hodge motive of this, and in particular…
In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…