The purpose of this paper is to study in greater detail the arithmetic KodairaSpencer morphism of an elliptic curve introduced in [Mzk1], Chapter IX, in the general context of the Hodge-Arakelov theory of elliptic curves, developed in [Mzk1-3]. In particular, after correcting a minor error (cf. Corollary 1.6) in the construction of this arithmetic Kodaira-Spencer morphism in [Mzk1], Chapter IX,...

Kontsevich’s formality theorem and the consequent star-product formula rely on the construction of an L∞-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential grade...

It is well-known that any morphism between two p-compact groups will lift, nonuniquely, to an admissible morphism between the maximal tori. We identify here a class of pcompact group morphisms, the p-toric morphisms, which can be perceived as generalized rational isomorphisms, enjoying the stronger property of lifting uniquely to a morphism between the maximal torus normalizers. We investigate ...

In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This phenomena appears in the case when we are using the Second-Order tuple-generating dependencies (SOtgd) with existentially quantified non-built-in functions, for th...

New representation results for three families of regular languages are stated, using a special kind of shuffle operation, namely the synchronized shuffle. First, it is proved that the family of regular star languages is the smallest family containing the language (a+ bc)∗ and closed under synchronized shuffle and length preserving morphism. The second representation result states that the famil...

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points. When the surface is the complex projective plane, we determine all the 1-point genus-0 Gromov-Witten invariants extremal with respect to the Gieseker-Uhlenbeck...

We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties. We assume that the map is an inclusion of codimension one. Then the existence of a morphism follows from Saito’s decomposition theorem. For varieties with conical singularities we show, that the existence of intersection homology morphism is exactly equivalent ...

Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small catego...