Related papers: Mixed Resolutions and Simplicial Sections
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…
This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We introduce the notion of a simultaneous categorical resolution of singularities, a categorical version of simultaneous resolutions of rational double points of surface degenerations. Furthermore, we suggest a construction of simultaneous…
After briefly recalling some computational aspects of blowing up and of representation of resolution data common to a wide range of desingularization algorithms (in the general case as well as in special cases like surfaces or binomial…
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…