We investigate conditions for simultaneous normalizability of a family of reduced schemes, i.e., the normalization of the total space normalizes, fiber by fiber, each member of the family. The main result (under more general conditions) is that a flat family of reduced equidimensional projective C-varieties (Xy)y∈Y with normal parameter space Y—algebraic or analytic—admits a simultaneous normal...

We present a purely domain-theoretic model of Coquand and Huet’s Calculus of Construction [3], which is one of the most powerful type systems proposed in the literature. The well-formed expressions of its language are divided into three levels: Terms, Types, and Orders. Terms are the elements of Types, while the elements of Orders are called Operators. There is a special Order constant Type den...

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient homeomorphism, and further that imply they are ambiently isotopic. Along way, we prove certain pairs of group, homeomorphic boundaries, equivalent equivariant int...

Assistant Professor, Department of Surgical Oncology, Acharya Tulsi Regional Cancer Treatment & Research Centre, Bikaner Consulting Oncosurgeon, Department of Surgical Oncology, Saviour Multispecialty Hospital, Ahmedabad Retd.Professor & Chief of Surgical Oncology, Department of Surgical Oncology, Gujarat Cancer & Research Institute, Ahmedabad Plastic Surgeon, Department of Surgical Oncology, G...

We study canonical central extensions of the general linear group ring adeles on a smooth projective algebraic surface $X$ by means integers. By these and adelic transition matrices rank $n$ locally free sheaf ${\mathcal O}_X$-modules we obtain local (adelic) decomposition for difference Euler characteristics this O}_X^n$. Two various calculations lead to Riemann-Roch theorem (without Noether f...

Budzyński and Kondracki ([3]) have introduced a notion of locally trivial quantum principal fibre bundle making use of an algebraic notion of covering, which allows a reconstruction of the bundle from local pieces. Following this approach, we construct covariant differential algebras and connections on locally trivial quantum principal fibre bundles by gluing together such locally given geometr...

1.1. It is well-known that an Anosov diffeomorphism is structurally stable: every C-diffeomorphism which is sufficiently close in C-topology to an Anosov diffeomorphism is topologically conjugate to it. However, the conjugation map is not differentiable in general. On the other hand, Anosov actions by higher rank abelian groups exhibit much more rigid behavior (see [93] for the first result of ...

1.1. Motivation. Over C and over non-archimedean fields, analytification of algebraic spaces is defined as the solution to a quotient problem. Such analytification is interesting, since in the proper case it beautifully explains the essentially algebraic nature of proper analytic spaces with “many” algebraically independent meromorphic functions. (See [A] for the complex-analytic case, and [C3]...