Patterns of Aggressive Behaviour and Victimization in Adolescents

The objective of the presented research was to find the family determinants for undertaking the aggressor or victim role. The obtained results enabled the description of environmental (family-related) and developmental factors that have a bearing on the formation of perpetrator or victim identity. For that purpose, two groups of variables were identified. The first group included child-independent variables shaping the socio-economic status of the family (parents’ education, material status, number of siblings), while the second group pertained to the patterns of attachment to each parent. The sample consisted of 120 adolescents aged 13 to 20. The research tools were Mini – DIA, the Inventory of Parent and Peer Attachment – IPPA, and Buss-Perry aggression questionnaire. The results revealed a number of determinants for persons involved in perpetration or victimization, such as the type of relationship with parents (secure or insecure pattern), personal experience of being in the victim or aggressor role, and the level of hostility. The resulting “determinant bundles” may inform professionals in their work with adolescents in the field of prevention or therapy.

SOME INDEX FORMULAE ON THE MODULI SPACE OF STABLE PARABOLIC VECTOR BUNDLES

We study natural families of $\bar {\partial } $-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

On the determinant bundles of abelian schemes

Let $\pi :\mathcal {A}\rightarrow S$ be an abelian scheme over a scheme S which is quasi-projective over an affine noetherian scheme and let $\mathcal {L}$ be a symmetric, rigidified, relatively ample line bundle on $\mathcal {A}$. We show that there is an isomorphism of line bundles on S, where d is the rank of the (locally free) sheaf $\pi _*{\cal L}$. We also show that the numbers 24 and 12d are sharp in the following sense: if N>1 is a common divisor of 12 and 24, then there are data as above such that

ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES

Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.