Search results for "Geometry"

Faithful representations of left C*-modules

2010

The existence of a faithful modular representation of a left module $$ \mathfrak{X} $$ over a C*-algebra $$ \mathfrak{A}_\# $$ possessing sufficiently many traces is proved.

New Families of Symplectic Runge-Kutta-Nyström Integration Methods

2001

We present new 6-th and 8-th order explicit symplectic Runge-Kutta-Nystrom methods for Hamiltonian systems which are more efficient than other previously known algorithms. The methods use the processing technique and non-trivial flows associated with different elements of the Lie algebra involved in the problem. Both the processor and the kernel are compositions of explicitly computable maps.

Fibred Categories and the Six Functors Formalism

2019

In Section 1, we introduce the basic language used in this book, the so-called premotivic categories and their functoriality. This is an extension of the classical notion of fibered categories. They appear with different categorical structures. In Section2, the language of premotivic categories is specialized to that of triangulated categories and to algebraic geometry. We introduce several axioms of such categories which ultimately will lead to the full six functors formalism. An emphasis is given on the study of the main axioms, with a special care about the so-called localization axiom. Then in Section 3, the general theory of descent is formulated in the language of premotivic model cat…

Double point curves for corank 2 map germs from C2 to C3

2012

Abstract We characterize finite determinacy of map germs f : ( C 2 , 0 ) → ( C 3 , 0 ) in terms of the Milnor number μ ( D ( f ) ) of the double point curve D ( f ) in ( C 2 , 0 ) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f t : ( C 2 , 0 ) → ( C 3 , 0 ) is equivalent to the constancy of both μ ( D ( f t ) ) and μ ( f t ( C 2 ) ∩ H ) with respect to t , where H ⊂ C 3 is a generic plane.

Tsen–Lang Theory for Cpi-fields

1995

Proper triangular Ga-actions on A^4 are translations

2013

We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3.

On many-sorted algebraic closure operators

2004

A theorem of Birkhoff-Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many-sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many-sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Asymptotically good codes from generalized algebraic-geometry codes

2005

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.

ON AUTOMORPHISMS OF GENERALIZED ALGEBRAIC-GEOMETRY CODES.

2007

Abstract We consider a class of generalized algebraic-geometry codes based on places of the same degree of a fixed algebraic function field over a finite field F / F q . We study automorphisms of such codes which are associated with automorphisms of F / F q .

A complete variety with infinitely many maximal quasi-projective open subsets. (English summary)

2010

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