Decomposable cycles and Noether-Lefschetz loci

We prove that there exist smooth surfaces of degree d in projective 3-space such that the group of rational equivalence classes of decomposable 0-cycles has rank at least the integer part of (d-1)/3.Comment: Exposition improve

Aesthetic value: beauty, ugliness and incoherence

[FIRST PARAGRAPHS] From Plato through Aquinas to Kant and beyond beauty has traditionally been considered the paradigmatic aesthetic quality. Thus, quite naturally following Socrates' strategy in The Meno, we are tempted to generalize from our analysis of the nature and value of beauty, a particular aesthetic value, to an account of aesthetic value generally. When we look at that which is beautiful, the object gives rise to a certain kind of pleasure within us. Thus aesthetic value is characterized in terms of that which affords us pleasure. Of course, the relation cannot be merely instrumental. Many activities may lead to consequent pleasures that we would not consider to be aesthetic in any way. For example, playing tennis, going swimming or finishing a book. Rather it is in the very contemplation of the object itself that we derive pleasure. As Kant puts it: We dwell on the contemplation of the beautiful because this contemplation strengthens and reproduces itself. The case is analogous (but analogous only) to the way we linger on a charm in the representation of an object which keeps arresting the attention, the mind all the while remaining passive. Thus contemporary philosophers have, following this tradition, defined aesthetic value in terms of our delighting in and savouring an object with pleasure.* An object is of intrinsic aesthetic value if it appropriately gives rise to pleasure in our contemplation of it. Of course background knowledge of particular art movements, cate- gories or artistic intentions may be required to perceive an artwork appropriately. Nonetheless, given the relevant understanding, it is in attending to and savouring uhat is presented to us that we are afforded pleasure

The Impact of English Language Proficiency and Workplace Readiness on the Employment Outcomes of Tertiary International Students (Executive Summary)

This project examines the influence of English language proficiency (ELP) on workplace readiness and employment outcomes for international students and graduates who seek to work in Australia. The study adopts a mixed method approach involving a detailed review of relevant literature, semi-structured individual interviews and focus groups, and quantitative analyses of three statistical data sets — Australian 2006 Census data, Australian Education International (AEI) data from January 2002 to June 2008, and the former Department of Immigration and Multicultural and Indigenous Affairs (DIMIA) Longitudinal Survey of Immigrants to Australia (October 2005 and October 2006). The qualitative data from the interviews enabled the authors to analyse the topic of investigation from several different perspectives including those of: international students and graduates; local (permanent resident or citizen) students and graduates; representatives of tertiary institutions and VET providers; recent offshore graduate job seekers with overseas qualifications; and Australian employers and regulatory bodies in five professional and three trade fields. The findings show that international students employment outcomes are not as good as their Australian domestic counterparts and that they face greater challenges in finding full-time employment after graduation. While ELP is a key factor influencing their employment outcomes — particularly if graduates have low levels of ELP — the findings from this study show that ELP is not the only or principal issue. Employers\u27 first priority is to engage graduates with strong profession-specific skills and then to consider their ‘well-roundedness’. The ‘well-roundedness’ includes graduates’ personal characteristics and attributes, the diversity of their experiences and skills, as well as their ‘cultural fit’ into the workplace. There is potential to respond to this expectation through policies and practices that support integrated approaches for enhancing ELP and workplace readiness within educational institutions, as well as increasing international students’ awareness of the value of the experiences and skills they can develop outside of their studies

Developing algebraic and didactical knowledge in pre-service primary teacher education

This study analyzes the contribution of a teaching experiment for the development of prospective primary teachers regarding knowledge of algebra and of algebra teaching as well as their professional identity. The case study of a prospective teachersuggests that an exploratory approach combining content and pedagogy supports this development, especially in the need to propose challenging tasks, to provide opportunity for students’ autonomous work and collective discussions and to be attentive to children’s representations and strategies in order to promote algebraic thinking

Literacy: Buzz Word on the Back Burner

This paper is reviews 12 published articles written on the importance of literacy in mathematics and the best practices to utilize inside the math classroom. The paper focuses on the definition of literacy of Orr, Kukner, and Timmons (2014), a definition that adapts literacy from reading and writing to the inclusion of problem solving, critical thinking, and the interaction with materials. The study conducted beyond the review of the literature was aimed at identifying the need for literacy across all content areas. The results of the findings show that as an educational community we show awareness of the deficit, but have not identified ways in which we may improve upon those deficits

Moduli of sheaves and the Chow group of K3 surfaces

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.Comment: Deleted a footnote and replaced it by a sentence in the main body of the pape