Abelian covers and isotrivial canonical fibrations

We classify all the surfaces of general type whose canonical map is composed with a pencil if they are the quotient of the diagonal action by an Abelian group acting over the product of two curves. As far as we know all the previous examples with isotrivial canonical map are very particular cases of our construction; moreover we find an unexpected action by a group of order 16. This construction can be easily generalizable to all dimensions.Comment: To Appear Comm. in Al

Generalized adjoint forms on algebraic varieties

We prove a full generalization of the Castelnuovo's free pencil trick. We show its analogies with the Adjoint Theorem; see L. Rizzi, F. Zucconi, Differential forms and quadrics of the canonical image, arXiv:1409.1826 and also Theorem 1.5.1 in G. P. Pirola, F. Zucconi, Variations of the Albanese morphisms, J. Algebraic Geom. 12 (2003), no. 3, 535-572. Moreover we find a new formulation of the Griffiths's infinitesimal Torelli Theorem for smooth projective hypersurfaces using meromorphic $1$-forms.Comment: 18 page

Doing research on the effectiveness of psychotherapy and psychotherapy training: a person-centered/experiential perspective

In this article, we present a framework for selecting instruments for evaluating psychotherapy and psychotherapy training from a person-centered and experiential psychotherapy (PCEP) perspective. The protocol is divided into eight therapy measurement domains, consisting of four research themes (therapy outcome, therapy process, client predictors, training outcome) and two levels (general/pan-theoretical concepts vs. treatment specific/PCEP-oriented concepts). This research protocol provides recommendations about what to measure, encouraging collaboration across different training sites, while still allowing flexibility for individual centers. Minimum and systematic case study data collection designs are described: Minimum designs are appropriate for use in private practice settings with one's own clients; systematic case-study designs can be used for student case-presentation requirements or for publication. The framework and research protocols described are part of an emerging international research project involving private and public training centers in several countries

Circle of Sarkisov links on a Fano 33-fold

For a general Fano $3$-fold of index $1$ in the weighted projective space $\mathbb{P}(1,1,1,1,2,2,3)$ we construct $2$ new birational models that are Mori fibre spaces, in the framework of the so-called Sarkisov program. We highlight a relation between the corresponding birational maps, as a circle of Sarkisov links, visualising the notion of relations (due to Kaloghiros) in Sarkisov program