Degenerations of K3 Surfaces of Degree Two

We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every fibre to either a sextic hypersurface in P(1,1,1,3) or a complete intersection of degree (2,6) in P(1,1,1,2,3). Furthermore, we find an explicit description of the hypersurfaces and complete intersections that can arise, thereby giving a full classification of the possible singular fibres.Comment: Final version. Accepted for publication by the Transactions of the American Mathematical Societ

ADE surfaces and their moduli

We define a class of surfaces corresponding to the ADE root lattices and construct compactifications of their moduli spaces as quotients of projective varieties for Coxeter fans, generalizing Losev-Manin spaces of curves. We exhibit modular families over these moduli spaces, which extend to families of stable pairs over the compactifications. One simple application is a geometric compactification of the moduli of rational elliptic surfaces that is a finite quotient of a projective toric variety.Comment: A streamlined and expanded versio

Stable pair compactification of moduli of K3 surfaces of degree 2

We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces in this family are described by integral-affine structures on a sphere with 24 singularities.Comment: v2: Updated reference

Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds

We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a so-called Tyurin degeneration to a union of two Fano varieties, then one should be able to construct a mirror to that Calabi-Yau by gluing together the Landau-Ginzburg models of those two Fano varieties. We provide evidence for this correspondence in a number of different settings, including Batyrev-Borisov mirror symmetry for K3 surfaces and Calabi-Yau threefolds, Dolgachev-Nikulin mirror symmetry for K3 surfaces, and an explicit family of threefolds that are not realized as complete intersections in toric varieties.Comment: v2: Section 5 has been completely rewritten to accommodate results removed from Section 5 of arxiv:1501.04019. v3: Final version, to appear in String-Math 2015, forthcoming volume in the Proceedings of Symposia in Pure Mathematics serie

Illuminating and measuring personal development: the impact of this work on learning and teaching

This short article gives an overview of a small-scale case study research project based on a 2nd year cohort of students from the Business Information Systems area of the School of Computing, Engineering and Information Sciences at Northumbria University. The aim of this employability module is to prepare students for the recruitment process for their placement year in industry and to inculcate proper professional attitudes and behaviour. The teaching strategy uses the precepts of PDP, and an eportfolio is the vehicle for learning and assessment

Mapping Joseph Furphy’s Riverina—Yooringa

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The Influence of Aluminium and Zinc upon the Absorption and Retention of Calcium and Phosphorus in Lambs

In recent years an increasing amount of attention has been given to the mineral fraction of feeds and to its importance in animal nutrition. As a result, it is now well-recognised that the value of a dietary source of an element depends not only upon its total content, but also upon the ability of the animal to extract that element and to retain it for use in metabolic processes. A considerable body of evidence now exists to show that the availability of the inorganic elements, to the animal, may differ widely in various livestock feeds and supplements. Insufficient data are available, however, to allow any great im-provement in the present system of recommending dietary allowances for min-erals, which is based upon the total content of the element with no allow-ance being made for the non-available fraction. In addition, it is be-coming apparent that the percentage availability or digestibility of an element is not a constant for a particular feed but varies with the species of animal, its age and past nutritional history and other factors. The introduction of suitable radioisotope procedures has made pos-sible a deeper understanding of the various metabolic processes associated with the ingestion and subsequent utilization and distribution of the in-organic elements. In addition, such methods have greatly helped in obtain-ing a more accurate estimate of the true digestibilIty of mineral elements in feeds under varying dietary and environmental conditions. Considerable data are now available from this type of study, particularly for the ele-ments calcium and phosphorus. Several reports exist which strongly suggest that interactions be-tween both the organic and inorganic constituents in the alimentary tract of an animal may increase or decrease calcium and phosphorus absorption. lt would therefore seem pertinent to study some of these possible effects upon availability and to estimate their magnitude. Little information is available regarding the effects of aluminium and zinc upon the availability of calcium and phosphorus in ruminants, though some does exist for laboratory animals. The element aluminium is of considerable interest in view of its suggested use as an alleviator in fluorine toxicity while the increasing nutritional roles of zinc, and the suggestion of a relationship to calcium in parakeratosis, make it an ele-ment worthy of study. The present investigation was conducted to determine the effects of dietary aluminium and zinc upon the absorption and retention of calcium and phosphorus in lambs. Conventional chemical and radiochemical balance ex-periments were made which allowed the calculation of data, for the net ab-sorption, endogenous fecal excretion and true digestibility of calcium and phosphorus

Here today, gone next week: some lessons for the delivery of itinerant primary schooling of a distance education program designed for the children of the Showmen's Guild of Australasia

This paper presents initial results of research on a distance education program developed in 1989 for the children of the Showmen's Guild of Australasia. The program accommodates the mobility of children and their parents who are rarely in any town for more than a week during the show circuit. The children complete correspondence lessons in various subjects and are assisted by their parents or home tutors. Several times a year, distance education teachers join the children during the show circuit and work intensively with them for several weeks. Unlike many other groups involved in the distance education program, the Showmen's Guild is well organized. It has a very supportive parent base and has campaigned over the years to establish favorable political support for a program to meet the special needs of its children. A literature review reveals that high mobility can place students at an educational disadvantage while placing an enormous burden on those providing the education for the mobile group. Interviews conducted with parents, children, home tutors, and teachers revealed close and trusting relationships between parents and distance education teachers and between students and distance education teachers. In addition, there is typically an intimate relationship between the mother and her children as it is the mother who takes on the responsibility for organizing and managing her children's education during a hectic working day. This paper concludes that the uniqueness of each mobile group must be taken into account when implementing an educational program, and delivery must respond to the socioeconomic and cultural attributes of each group. (LP

Families of lattice polarized K3 surfaces with monodromy

We extend the notion of lattice polarization for K3 surfaces to families over a (not necessarily simply connected) base, in a way that gives control over the action of monodromy on the algebraic cycles, and discuss the uses of this new theory in the study of families of K3 surfaces admitting fibrewise symplectic automorphisms. We then give an application of these ideas to the study of Calabi-Yau threefolds admitting fibrations by lattice polarized K3 surfaces