471 research outputs found
Del Pezzo surfaces of degree 1 and jacobians
We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves,
using Del Pezzo surfaces of degree 1. This paper is a natural continuation of
author's paper math.AG/0405156.Comment: 24 page
Two-parametric deformation and its induced representations
The two-parametric quantum superalgebra is consistently
defined. A construction procedure for induced representations of
is described and allows us to construct explicitly all
(typical and nontypical) finite-dimensional representations of this quantum
superalgebra. In spite of some specific features, the present approach is
similar to a previously developed method [1] which, as shown here, is
applicable not only to the one-parametric quantum deformations but also to the
multi-parametric ones.Comment: Latex, 13 pages, no figur
Research potential as a basis for innovative development of the region
Purpose of work is to determine an amount of influence from region’s innovative activity on effective usage of current scientific-research potential. Innovative activity of regions in many respects depends on the availability and efficient use of the existing research capacity. The main components of the research capacities in the region are: interest of universities, employers and society in research and development and their implementation in practice; development of research infrastructure; and a focus of higher education on the innovative activity of students; financial and tax support of enterprises engaged in innovative activities, from the stat
Covariant differential complexes on quantum linear groups
We consider the possible covariant external algebra structures for Cartan's
1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates:
1. the invariant 1-forms realize an adjoint representation of quantum group;
2. all monomials of these forms possess the unique ordering.
For the obtained external algebras we define the exterior derivative
possessing the usual nilpotence condition, and the generally deformed version
of Leibniz rules. The status of the known examples of GL_q(N)-differential
calculi in the proposed classification scheme, and the problems of
SL_q(N)-reduction are discussed.Comment: 23 page
Cohomology Groups of Deformations of Line Bundles on Complex Tori
The cohomology groups of line bundles over complex tori (or abelian
varieties) are classically studied invariants of these spaces. In this article,
we compute the cohomology groups of line bundles over various holomorphic,
non-commutative deformations of complex tori. Our analysis interpolates between
two extreme cases. The first case is a calculation of the space of
(cohomological) theta functions for line bundles over constant, commutative
deformations. The second case is a calculation of the cohomologies of
non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe
Old and New Fields on Super Riemann Surfaces
The ``new fields" or ``superconformal functions" on super Riemann
surfaces introduced recently by Rogers and Langer are shown to coincide with
the Abelian differentials (plus constants), viewed as a subset of the functions
on the associated super Riemann surface. We confirm that, as originally
defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new
reference
On representations of super coalgebras
The general structure of the representation theory of a -graded
coalgebra is discussed. The result contains the structure of Fourier analysis
on compact supergroups and quantisations thereof as a special case. The general
linear supergroups serve as an explicit illustration and the simplest example
is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-
Labels for non-individuals
Quasi-set theory is a first order theory without identity, which allows us to
cope with non-individuals in a sense. A weaker equivalence relation called
``indistinguishability'' is an extension of identity in the sense that if
is identical to then and are indistinguishable, although the
reciprocal is not always valid. The interesting point is that quasi-set theory
provides us a useful mathematical background for dealing with collections of
indistinguishable elementary quantum particles. In the present paper, however,
we show that even in quasi-set theory it is possible to label objects that are
considered as non-individuals. We intend to prove that individuality has
nothing to do with any labelling process at all, as suggested by some authors.
We discuss the physical interpretation of our results.Comment: 11 pages, no figure
Minkowski superspaces and superstrings as almost real-complex supermanifolds
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that
mathematicians study are real or (almost) complex ones, while Minkowski
superspaces are completely different objects. They are what we call almost
real-complex supermanifolds, i.e., real supermanifolds with a non-integrable
distribution, the collection of subspaces of the tangent space, and in every
subspace a complex structure is given.
An almost complex structure on a real supermanifold can be given by an even
or odd operator; it is complex (without "always") if the suitable superization
of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we
define the circumcised analog of the Nijenhuis tensor. We compute it for the
Minkowski superspaces and superstrings. The space of values of the circumcised
Nijenhuis tensor splits into (indecomposable, generally) components whose
irreducible constituents are similar to those of Riemann or Penrose tensors.
The Nijenhuis tensor vanishes identically only on superstrings of
superdimension 1|1 and, besides, the superstring is endowed with a contact
structure. We also prove that all real forms of complex Grassmann algebras are
isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to
related recent work by Witten is adde
Duality for the Jordanian Matrix Quantum Group
We find the Hopf algebra dual to the Jordanian matrix quantum group
. As an algebra it depends only on the sum of the two parameters
and is split in two subalgebras: (with three generators) and
(with one generator). The subalgebra is a central Hopf subalgebra of
. The subalgebra is not a Hopf subalgebra and its coalgebra
structure depends on both parameters. We discuss also two one-parameter special
cases: and . The subalgebra is a Hopf algebra and
coincides with the algebra introduced by Ohn as the dual of . The
subalgebra is isomorphic to as an algebra but has a
nontrivial coalgebra structure and again is not a Hopf subalgebra of
.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC
nonlinear ma
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