353 research outputs found
Hodge polynomials of some moduli spaces of Coherent Systems
When , we study the coherent systems that come from a BGN extension in
which the quotient bundle is strictly semistable. In this case we describe a
stratification of the moduli space of coherent systems. We also describe the
strata as complements of determinantal varieties and we prove that these are
irreducible and smooth. These descriptions allow us to compute the Hodge
polynomials of this moduli space in some cases. In particular, we give explicit
computations for the cases in which and is even,
obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of
coherent systems on algebraic curves and their Hodge--Poincar\'e
polynomials". The paper has been substantially shorten. Theorem 8.20 has been
revised and corrected. Final version accepted for publication in
International Journal of Mathematics. arXiv admin note: text overlap with
arXiv:math/0407523 by other author
Seshadri constants and Grassmann bundles over curves
Let be a smooth complex projective curve, and let be a vector bundle
on which is not semistable. For a suitably chosen integer , let
be the Grassmann bundle over that parametrizes the quotients
of the fibers of of dimension . Assuming some numerical conditions on
the Harder-Narasimhan filtration of , we study Seshadri constants of ample
line bundles on . In many cases, we give the precise value of
Seshadri constant. Our results generalize various known results for .Comment: Final version; Annales Inst. Fourier (to appear
Moduli spaces of coherent systems of small slope on algebraic curves
Let be an algebraic curve of genus . A coherent system on
consists of a pair , where is an algebraic vector bundle over of
rank and degree and is a subspace of dimension of the space of
sections of . The stability of the coherent system depends on a parameter
. We study the geometry of the moduli space of coherent systems for
. We show that these spaces are irreducible whenever they are
non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction
Universal families on moduli spaces of principal bundles on curves
Let H be a connected semisimple linear algebraic group defined over C and X a compact connected Riemann surface of genus at least three. Let M'X(H) be the moduli space parametrising all topologically trivial stable principal H-bundles over X whose automorphism group coincides with the centre of H. It is a Zariski open dense subset of the moduli space of stable principal H-bundles. We prove that there is a universal principal H-bundle over X × M'X(H) if and only if H is an adjoint group (i.e., the centre of H is trivial)
Quantization of Fayet-Iliopoulos Parameters in Supergravity
In this short note we discuss quantization of the Fayet-Iliopoulos parameter
in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos
parameter determines a lift of the group action to a line bundle, and such
lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted
in terms of moment maps and symplectic reductions, we argue that in
supergravity the quantization of the Fayet-Iliopoulos parameter has a natural
understanding in terms of linearizations in geometric invariant theory (GIT)
quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe
Struggling and juggling: a comparison of assessment loads in research and teaching-intensive universities
In spite of the rising tide of metrics in UK higher education, there has been scant attention paid to assessment loads, when evidence demonstrates that heavy demands lead to surface learning. Our study seeks to redress the situation by defining assessment loads and comparing them across research-and teaching intensive universities. We clarify the concept of âassessment loadâ in response to findings about high volumes of summative assessment on modular degrees. We define assessment load across whole undergraduate degrees, according to four measures: the volume of summative assessment; volume of formative assessment; proportion of examinations to coursework; number of different varieties of assessment. All four factors contribute to the weight of an assessment load, and influence studentsâ approaches to learning. Our research compares programme assessment data from 73 programmes in 14 UK universities, across two institutional categories. Research-intensives have higher summative assessment loads and a greater proportion of examinations; teaching-intensives have higher varieties of assessment. Formative assessment does not differ significantly across both university groups. These findings pose particular challenges for students in different parts of the sector. Our study questions the wisdom that âmoreâ is always better, proposing that lighter assessment loads may make room for âslowâ and deep learning
Elemental boron doping behavior in silicon molecular beam epitaxy
Boron-doped Si epilayers were grown by molecular beam epitaxy (MBE) using an elemental boron source, at levels up to 2Ă1020 cmâ3, to elucidate profile control and electrical activation over the growth temperature range 450â900 °C. Precipitation and surface segregation effects were observed at doping levels of 2Ă1020 cmâ3 for growth temperatures above 600 °C. At growth temperatures below 600 °C, excellent profile control was achieved with complete electrical activation at concentrations of 2Ă1020 cmâ3, corresponding to the optimal MBE growth conditions for a range of Si/SixGe1âx heterostructures
Brauer group of moduli spaces of pairs
We show that the Brauer group of any moduli space of stable pairs with fixed
determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr
A functorial construction of moduli of sheaves
We show how natural functors from the category of coherent sheaves on a
projective scheme to categories of Kronecker modules can be used to construct
moduli spaces of semistable sheaves. This construction simplifies or clarifies
technical aspects of existing constructions and yields new simpler definitions
of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in
Inventiones Mathematicae. Slight change in the definition of the Kronecker
algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations
elsewhere, to make the constructions work for non-reduced schemes. Section
6.5 rewritten. Remark 2.6 and new references adde
Embedding technology in translation teaching:evaluative considerations for courseware integration
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