Groupoids and the Brauer group
Groups with large Noether bound
The finite groups having an indecomposable polynomial invariant of degree at least half the order of the group are classified. It turns out that –apart from four sporadic exceptions– these are exactly the groups with a cyclic subgroup of index at most two.
Growth of Betti Numbers over Noetherian Local Rings.
Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations
Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations
We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows.Let be an element of a Hardy field which has an asymptotic series expansion in , and ,...
Hadamard operations on rational functions
Hardy fields in several variables
In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia , la sua chiusura algebrica relativa nell'anello , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale del campo...
Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
In this paper we prove that the projective dimension of is , where is the ring of polynomials in variables with complex coefficients, and is the module generated by the columns of a matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of quaternionic variables. As a corollary we show that the sheaf of regular functions has flabby dimension , and we prove a cohomology vanishing theorem for open...
Hasse–Schmidt derivations, divided powers and differential smoothness
Let be a commutative ring, a commutative -algebra and the filtered ring of -linear differential operators of . We prove that: (1) The graded ring admits a canonical embedding into the graded dual of the symmetric algebra of the module of differentials of over , which has a canonical divided power structure. (2) There is a canonical morphism from the divided power algebra of the module of -linear Hasse–Schmidt integrable derivations of to . (3) Morphisms and fit into a...
Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze
We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion...
Heinrich's counterexample to Azevedo's conjecture.
Hereditary tensor-orthogonal theories
Hermitesche und orthogonale Operatoren über kommutativen Ringen.
Higher Kodaira-Spencer classes.
Higher order differentials and Weierstrass points on Gorenstein curves.
Higher ramification in Hensel fields.
Higher-dimensional cluster combinatorics and representation theory
Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite-dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection...
Hilbert functions, Castelnuovo-Mumford regularity and uniform Artin-Rees numbers.
Hilbert functions on Cohen-Macaulay ideals with assigned generators’ degrees
Hilbert rings and the chain condition for prime ideals.