scholarly journals A support theorem for the Hitchin fibration: the case of

2017 ◽  
Vol 153 (6) ◽  
pp. 1316-1347
Author(s):  
Mark Andrea de Cataldo

We prove that the direct image complex for the $D$-twisted $\text{SL}_{n}$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for $\text{GL}_{n}$ is due to Chaudouard and Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove $\unicode[STIX]{x1D6FF}$-regularity results for some auxiliary weak abelian fibrations.

Author(s):  
Mark Andrea A. de Cataldo ◽  
Jochen Heinloth ◽  
Luca Migliorini

Abstract We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL n {\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n ≥ 2 {n\geq{2}} . A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves.


2021 ◽  
Vol 157 (4) ◽  
pp. 835-882
Author(s):  
Luca Migliorini ◽  
Vivek Shende ◽  
Filippo Viviani

We study the cohomology of Jacobians and Hilbert schemes of points on reduced and locally planar curves, which are however allowed to be singular and reducible. We show that the cohomologies of all Hilbert schemes of all subcurves are encoded in the cohomologies of the fine compactified Jacobians of connected subcurves, via the perverse Leray filtration. We also prove, along the way, a result of independent interest, giving sufficient conditions for smoothness of the total space of the relative compactified Jacobian of a family of locally planar curves.


2018 ◽  
Vol 41 ◽  
Author(s):  
Maria Babińska ◽  
Michal Bilewicz

AbstractThe problem of extended fusion and identification can be approached from a diachronic perspective. Based on our own research, as well as findings from the fields of social, political, and clinical psychology, we argue that the way contemporary emotional events shape local fusion is similar to the way in which historical experiences shape extended fusion. We propose a reciprocal process in which historical events shape contemporary identities, whereas contemporary identities shape interpretations of past traumas.


2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.


1976 ◽  
Vol 32 ◽  
pp. 233-254
Author(s):  
H. M. Maitzen

Ap stars are peculiar in many aspects. During this century astronomers have been trying to collect data about these and have found a confusing variety of peculiar behaviour even from star to star that Struve stated in 1942 that at least we know that these phenomena are not supernatural. A real push to start deeper theoretical work on Ap stars was given by an additional observational evidence, namely the discovery of magnetic fields on these stars by Babcock (1947). This originated the concept that magnetic fields are the cause for spectroscopic and photometric peculiarities. Great leaps for the astronomical mankind were the Oblique Rotator model by Stibbs (1950) and Deutsch (1954), which by the way provided mathematical tools for the later handling pulsar geometries, anti the discovery of phase coincidence of the extrema of magnetic field, spectrum and photometric variations (e.g. Jarzebowski, 1960).


Author(s):  
W.M. Stobbs

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.


1979 ◽  
Vol 44 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Carol A. Pruning

A rationale for the application of a stage process model for the language-disordered child is presented. The major behaviors of the communicative system (pragmatic-semantic-syntactic-phonological) are summarized and organized in stages from pre-linguistic to the adult level. The article provides clinicians with guidelines, based on complexity, for the content and sequencing of communicative behaviors to be used in planning remedial programs.


ASHA Leader ◽  
2013 ◽  
Vol 18 (2) ◽  
pp. 5-7 ◽  
Author(s):  
Patty Prelock

Children with disabilities benefit most when professionals let families lead the way.


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