A GIT interpretration of the Harder-Narasimhan filtration

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.Comment: 19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutens

X-ray spectra reveal the reawakening of the repeat changing-look AGN NGC 1566

We present simultaneous XMM-Newton and NuSTAR observations of the repeat changing-look AGN NGC 1566, which dramatically increased in brightness in the IR to X-ray bands in 2018. The broad-band X-ray spectrum was taken at the peak of the outburst and is typical of Seyfert 1 AGN. The spectrum shows a soft excess, Compton hump, warm absorption and reflection, ruling out tidal disruption as the cause of the outburst and demonstrating that a 'standard' accretion disk can develop very rapidly. The high resolution grating spectrum reveals that the outburst has launched a ~ 500 km/s outflow, and shows photoionised emission lines from rest-frame gas. We discuss possible mechanisms for the outburst, and conclude that it is most likely caused by a disk instability.Comment: 5 pages, 2 figures, accepted to MNRAS letter

Runaway and Hypervelocity Stars from Compact Object Encounters in Globular Clusters

The dense environments in the cores of globular clusters (GCs) facilitate many strong dynamical encounters among stellar objects. These encounters have been shown capable of ejecting stars from the host GC, whereupon they become runaway stars, or hypervelocity stars if unbound to the galactic potential. We study high speed stellar ejecta originating from GCs by using Monte Carlo N-body models, in particular focusing on binary-single encounters involving compact objects. We pair our model-discriminated populations with observational catalogs of Milky Way GCs to compose a present-day galactic population of stellar ejecta. We find that these kinds of encounters can accelerate stars to velocities in excess of 2000 km/s, to speeds beyond the previously predicted limits for ejecta from star-only encounters and in the same regime of galactic center ejections. However, the same ejections can only account for 1.5-20% of the total population of stellar runaways, and only 0.0001-1% of hypervelocity stars, with similar relative rates found for runaway white dwarfs. We also provide credible regions for ejecta from 149 Milky Way GCs, which we hope will be useful as supplementary evidence when pairing runaway stars with origin GCs.Comment: 16 pages, 11 figures, accepted for publication in Ap

Automorphisms of moduli spaces of vector bundles over a curve

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that the automorphism group of M(r,\Lambda) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.Comment: 12 page

Papiloma de plexo coroideo del cuarto ventrículo cerebral : diagnóstico y tratamiento quirúrgico

Se trata de una perra mestiza, de ocho años de edad y unos 30 kg de peso, con hemiparesis e inclinación de la cabeza hacia el lado izquierdo. Tras realizar una resonancia magnética nuclear (RMN) se identificó la lesión, compatible con una neoplasia, en fosa posterior a nivel del cuarto ventrículo cerebral. El tratamiento quirúrgico consistió en una craneotomía suboccipital que permitió el acceso a la fosa posterior, para poder así extraer el tumor. El resultado obtenido tras la cirugía se puede considerar satisfactorio, si tenemos en cuenta el alto grado de morbilidad que supone trabajar en esta regiónHerein, we report the case of an eight-year-old, 30 kg, female mixed-breed dog, with hemiparesis and left head tilt. Magnetic resonance imaging led to identify the lession as a tumor in the caudal fossa of the fourth ventricle. The surgical treatment consisted of a suboccipital craniotomy, which allowed the access to the caudal fossa, and the xtirpation of the tumor. A satisfactory result was achieved after the surgery, if we consider the high sick rate involved when working in this region

Rheological modelling of enzymatic extrusion of rice starch

A rice starch mixture pre-mixed with thermostable α-amylase was extruded in a pilot co-rotating twin-screw extruder, with the die replaced by a slit rheometer. The apparent viscosity at the slit wall was determined for a variety of operating conditions. The factors studied were barrel temperature (70–110 °C), water content (550–650 g/kg rice mixture), flow rate (8 × 10−7 to 2.5 × 10−6 m3/s) and enzyme concentration (0·01–0·1 g/kg). The same screw configuration and rotational speed (225 rpm) were used. A rheological model incorporating the integrated effect of extrusion and enzymatic activity was developed with a stepwise regression of the experimental data, analysing after each step the variability of the model parameters with the different factors. It was found that for the range of experimental conditions in question the influence of each factor could be considered separately with good results, leading to a power-law type model with a constant behaviour index. The parameters obtained describing the influence of water content, temperature and shear rate were within the range of available literature data for non-enzymatic extrusion and the influence of the enzyme concentration was well described by a power-law dependency

Comparison of Poisson structures on moduli spaces

Let $X$ be a complex irreducible smooth projective curve, and let ${\mathbb L}$ be an algebraic line bundle on $X$ with a nonzero section $\sigma_0$. Let $\mathcal{M}$ denote the moduli space of stable Hitchin pairs $(E,\, \theta)$, where $E$ is an algebraic vector bundle on $X$ of fixed rank $r$ and degree $\delta$, and $\theta\, \in\, H^0(X,\, End(E)\otimes K_X\otimes{\mathbb L})$. Associating to every stable Hitchin pair its spectral data, an isomorphism of $\mathcal{M}$ with a moduli space $\mathcal{P}$ of stable sheaves of pure dimension one on the total space of $K_X\otimes{\mathbb L}$ is obtained. Both the moduli spaces $\mathcal{P}$ and $\mathcal{M}$ are equipped with algebraic Poisson structures, which are constructed using $\sigma_0$. Here we prove that the above isomorphism between $\mathcal{P}$ and $\mathcal{M}$ preserves the Poisson structures