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.
Hilbert series and applications to graded rings.
Hilbert series of the Grassmannian and -Narayana numbers
We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the -Hilbert series is a Vandermonde-like determinant. We show that the -polynomial of the Grassmannian coincides with the -Narayana polynomial. A simplified formula for the -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the -Narayana numbers, i.e. the -polynomial...
Hilbert-Kunz function of monomial ideals and binomial hypersurfaces.
Hilbert-Poincaré series of bigraded algebras
Lo scopo di questo lavoro è la descrizione di alcune nuove tecniche per calcolare serie di Hilbert-Poincaré (HP-serie) di algebre standard, che possono essere viste come sottoalgebre di algebre bigraduate. In particolare mostriamo come calcolare in modo uniforme le HP-serie delle potenze di un idele omogeneo. Mostriamo anche come calcolare le HP-serie di prodotti di Segre e di alcune algebre di Blow-up, che sono di interesse in Geometria Algebrica. Per alcune classi siamo in grado di descrivere...
Histoire de la loi de réciprocité quadratique : Gauss et Tate