1,278 research outputs found
Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a K3 surface
Let M be a 2n-dimensional Kahler manifold deformation equivalent to the
Hilbert scheme of length n subschemes of a K3 surface S. Let Mon be the group
of automorphisms of the cohomology ring of M, which are induced by monodromy
operators. The second integral cohomology of M is endowed with the
Beauville-Bogomolov bilinear form. We prove that the restriction homomorphism
from Mon to the isometry group O[H^2(M)] is injective, for infinitely many n,
and its kernel has order at most 2, in the remaining cases. For all n, the
image of Mon in O[H^2(M)] is the subgroup generated by reflections with respect
to +2 and -2 classes. As a consequence, we get counter examples to a version of
the weight 2 Torelli question, when n-1 is not a prime power.Comment: Version 3: Latex, 54 pages. Expository change
Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type
Let X be a compact Kahler holomorphic-symplectic manifold, which is
deformation equivalent to the Hilbert scheme of length n subschemes of a K3
surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L)
vanishes and c_1(L) is primitive. Assume that the two dimensional subspace
H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex
coefficients, intersects trivially the integral cohomology. We prove that the
linear system of L is base point free and it induces a Lagrangian fibration on
X. In particular, the line-bundle L is effective. A determination of the
semi-group of effective divisor classes on X follows, when X is projective. For
a generic such pair (X,L), not necessarily projective, we show that X is
bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion
sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated
improvement to the exposition and corrected typos according to the referees
suggestions. To appear in the proceedings of the conference Algebraic and
Complex Geometry, Hannover 201
Multi-Hamiltonian structures for r-matrix systems
For the rational, elliptic and trigonometric r-matrices, we exhibit the links
between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of
matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral
curves and sheaves supported on them; (c) Symmetric products of a surface. We
have, at each level, a linear space of compatible Poisson structures, and the
maps relating the levels are Poisson. This leads in a natural way to Nijenhuis
coordinates for these spaces. At level (b), there are Hamiltonian systems on
these spaces which are integrable for each Poisson structure in the family, and
which are such that the Lagrangian leaves are the intersections of the
symplective leaves over the Poisson structures in the family. Specific examples
include many of the well-known integrable systems.Comment: 26 pages, Plain Te
Curve classes on irreducible holomorphic symplectic varieties
We prove that the integral Hodge conjecture holds for 1-cycles on irreducible
holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As
an application, we give a new proof of the integral Hodge conjecture for cubic
fourfolds.Comment: 15 page
Genetic Sensitivity Predicts Long-Term Psychological Benefits of a Relationship Education Program for Married Couples
Mothers' beliefs about infant teething in Enugu, South-east Nigeria: a cross sectional study
<p>Abstract</p> <p>Background</p> <p>Parents and Health Care Workers have traditionally attributed a variety of symptoms to teething in young children. Some of these symptoms may however connote underlying serious medical condition in a child. There is little evidence to support these beliefs despite their implications on management of a symptomatic teething child. This study therefore seeks determine the beliefs and problems mothers associate with teething in Enugu, South-east Nigeria.</p> <p>Findings</p> <p>A cross-sectional survey involving sixty mothers presenting at a Children's clinic in Enugu metropolis using questionnaire. More than 90% of the respondents thought that babies can experience medical problems as a result of teething. The commonest medical problems perceived to be associated with teething were fever (71.7%), loose stools (58.3%) and vomiting (35%).</p> <p>Conclusion</p> <p>Mothers still associate a variety of symptoms of childhood illnesses to teething and this association is not evidence based and could lead to delayed interventions, increased morbidity and mortality of children. It is important therefore that mothers and health workers caring for young children are educated on the need to seek prompt medical attentions in a symptomatic child.</p
The blurring boundaries between synchronicity and asynchronicity:new communicative situations in work-related Instant Messaging
Instant messaging is one of the most popular communication technologies in virtual teams, enabling interactions to intertwine whole working days, thus creating the sense of copresence for team members who are geographically dispersed. Through close linguistic analyses of naturally occurring data from a virtual team, this article discusses the implications of two novel communicative situations enabled by instant messaging: presence information and the persistence of transcript. The preliminary findings of this study indicate that these new communicative situations require the flouting or rethinking of previously existing interactional norms and that communicative practices employed by the team members are not yet conventionalized/normalized, the expectations and interpretations of interactional rituals and timing vary highly, even within the same virtual team
On Integrable Systems and Supersymmetric Gauge Theories
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten
hypothesis are discussed. The main ingredients of the formulation of the
finite-gap solutions to integrable equations in terms of complex curves and
generating 1-differential are presented, the invariant sense of these
definitions is illustrated. Recently found exact nonperturbative solutions to
N=2 SUSY gauge theories are formulated using the methods of the theory of
integrable systems and where possible the parallels between standard quantum
field theory results and solutions to integrable systems are discussed.Comment: LaTeX, 38 pages, no figures; based on the lecture given at INTAS
School on Advances in Quantum Field Theory and Statistical Mechanics, Como,
Italy, 1996; minor changes, few references adde
Dualities in integrable systems and N=2 theories
We discuss dualities of the integrable dynamics behind the exact solution to
the N=2 SUSY YM theory. It is shown that T duality in the string theory is
related to the separation of variables procedure in dynamical system. We argue
that there are analogues of S duality as well as 3d mirror symmetry in the
many-body systems of Hitchin type governing low-energy effective actions.Comment: 16 pages, Latex, Talk given at QFTHEP-99, Moscow, May 27-June
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