A simple limit for slope instability

Ross and Thomas have shown that subschemes can K-destabilise polarised varieties, yielding a notion known as slope (in)stability for varieties. Here we describe a special situation in which slope instability for varieties (for example of general type) corresponds to a slope instability type condition for certain bundles, making the computations almost trivial.Comment: 11 page

Solutions to Donaldson's hyperkaehler reduction on a curve

We study an infinite-dimensional hyperk\ue4hler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a Riemann surface. It is known that the corresponding moment map equations admit special solutions constructed from holomorphic quadratic differentials. Here we obtain a more general existence result and so a larger hyperk\ue4hler moduli space

Block-Goettsche invariants from wall-crossing

We show how some of the refined tropical counts of Block and Goettsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative q-deformed Gromov-Witten invariants. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined

Attempts to detect retrotransposition and de novo deletion of Alus and other dispersed repeats at specific loci in the human genome

Dispersed repeat elements contribute to genome instability by de novo insertion and unequal recombination between repeats. To study the dynamics of these processes, we have developed single DNA molecule approaches to detect de novo insertions at a single locus and Alu-mediated deletions at two different loci in human genomic DNA. Validation experiments showed these approaches could detect insertions and deletions at frequencies below 10(-6) per cell. However, bulk analysis of germline (sperm) and somatic DNA showed no evidence for genuine mutant molecules, placing an upper limit of insertion and deletion rates of 2 x 10(-7) and 3 x 10(-7), respectively, in the individuals tested. Such re-arrangements at these loci therefore occur at a rate lower than that detectable by the most sensitive methods currently available

A construction of Frobenius manifolds from stability conditions

© 2018 London Mathematical Society A finite quiver Q without loops or 2-cycles defines a CY3 triangulated category D(Q) and a finite heart A(Q)⊂D(Q). We show that if Q satisfies some (strong) conditions, then the space of stability conditions (A(Q))) supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in D(Q). In the case of An evaluating the family at a special point, we recover a branch of the Saito Frobenius structure of the An singularity y2=xn+1. We give examples where applying the construction to each mutation of Q and evaluating the families at a special point yields a different branch of the maximal analytic continuation of the same semisimple Frobenius manifold. In particular, we check that this holds in the case of An, n5

A Special Issue (Part-II): mafic-ultramafic rocks andalkaline-carbonatitic magmatism and associated hydrothermalmineralization – dedication to Lia N. Kogarko

Thisisthesecondpartofatwo-volumespecialis- sue of Open Geoscience (formerly Central European Jour- nal of Geosciences) that aims to be instrumental in pro- viding an update of Mac-Ultramac Rocks and Alkaline

Torus equivariant K-stability

It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds

Determination of zeolite-group mineral compositions by electron probe microanalysis

A new protocol for the quantitative determination of zeolite-group mineral compositions by electron probe microanalysis (wavelength-dispersive spectrometry) under ambient conditions, is presented. The method overcomes the most serious challenges for this mineral group, including new confidence in the fundamentally important Si-Al ratio. Development tests were undertaken on a set of natural zeolite candidate reference samples, representing the compositional extremes of Na, K, Cs, Mg, Ca, Sr and Ba zeolites, to demonstrate and assess the extent of beam interaction effects on each oxide component for each mineral. These tests highlight the variability and impact of component mobility due to beam interaction, and show that it can be minimized with recommended operating conditions of 15 kV, 2 nA, a defocused, 20 μm spot size, and element prioritizing with the spectrometer configuration. The protocol represents a pragmatic solution that works, but provides scope for additional optimization where required. Vital to the determination of high-quality results is the attention to careful preparations and the employment of strict criteria for data reduction and quality control, including the monitoring and removal of non-zeolitic contaminants from the data (mainly Fe and clay phases). Essential quality criteria include the zeolite-specific parameters of R value (Si/(Si + Al + Fe3+), the ‘E%’ charge-balance calculation, and the weight percent of non-hydrous total oxides. When these criteria are applied in conjunction with the recommended analytical operating conditions, excellent inter-batch reproducibility is demonstrated. Application of the method to zeolites with complex solid-solution compositions is effective, enabling more precise geochemical discrimination for occurrence-composition studies. Phase validation for the reference set was conducted satisfactorily with the use of X-ray diffraction and laser-ablation inductively-coupled plasma mass spectroscopy