Related papers: Adjoint Computation for Hypersurfaces Using Formal…
In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there…
We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…
We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular…
In this paper we discuss the desingularization algorithm for a toric surface. In particular, we construct an iterable method of determining the Hirzebruch-Jung continued fraction decomposition. These results are then applied to weighted…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…
Utilizing previously established results concerning costratification in relative tensor-triangular geometry, we classify the colocalizing subcategories of the singularity category of a locally hypersurface ring and then we generalize this…
We obtain sharp estimates on the connectivity of complex affine hypersurfaces in terms of the decomposition of the defining equation as a sum of weighted homogeneous components relative to some weight system.
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
A simplicial set is said to be non-singular if the representing map of each non-degenerate simplex is degreewise injective. The inclusion into the category of simplicial sets, of the full subcategory whose objects are the non-singular…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
In this note we present an $\infty$-categorical framework for descent along adjunctions and a general formula for counting conjugates up to equivalence which unifies several known formulae from different fields.
It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primitive functors, returns the usual adjunction between…
This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
This paper synergizes the roles of adjoint in various disciplines of mathematics, sciences, and engineering. Though the materials developed and presented are not new -- as each or some could be found in (or inferred from) publications in…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…