186 research outputs found
Categorial mirror symmetry for K3 surfaces
We study the structure of a modified Fukaya category
associated with a K3 surface , and prove that whenever is an elliptic K3
surface with a section, the derived category of \fF(X) is equivalent to a
subcategory of the derived category of coherent sheaves on
the mirror K3 surface .Comment: 11 pages, AmsLatex. Exposition (hopefully) improved, one argument
simplifie
A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces
We define a Fourier-Mukai transform for sheaves on K3 surfaces over \C, and
show that it maps polystable bundles to polystable ones. The role of ``dual''
variety to the given K3 surface is here played by a suitable component
of the moduli space of stable sheaves on . For a wide class of K3
surfaces can be chosen to be isomorphic to ; then the Fourier-Mukai
transform is invertible, and the image of a zero-degree stable bundle is
stable and has the same Euler characteristic as .Comment: Revised version, 15 pages AMSTeX with AMSppt.sty v. 2.1
Introduction to Fourier-Mukai and Nahm transforms with an application to coherent systems on elliptic curves
These notes record, in a slightly expanded way, the lectures given by the first two authors at the College on Moduli Spaces of Vector Bundles that took place at CIMAT in Guanajuato, Mexico, from November 27th to December 8th, 2006. The college, together with the ensuing conference on the same topic, was held in occasion of Peter Newstead's 65th anniversary. It has been a great pleasure and a privilege to contribute to celebrate Peter's outstanding achievements in algebraic geometry and his lifelong dedication to the progress of mathematical knowledge. We warmly thank the organizers of the college and conference for inviting us, thus allowing us to participate in Peter's celebration. The main emphasis in these notes is on the Fourier-Mukai transforms as equivalences of derived categories of coherent sheaves on algebraic varieties. For this reason, the first Section is devoted to a basic (but we hope, understandable) introduction to derived categories. In the second Section we develop the basic theory of Fourier-Mukai transforms. Another aim of our lectures was to outline the relations between Fourier-Mukai and Nahm transforms. This is the topic of Section 3. Finally, Section 4 is devoted to the application of the theory of Fourier-Mukai transforms to the study of coherent systems. This is a review paper. Most of the material is taken from [BBH08] and [HT08], although the presentation is different in some places
On the irreducibility of some quiver varieties
We prove that certain quiver varieties are irreducible and therefore are isomor-phic to Hilbert schemes of points of the total spaces of the bundles OP1( 12n) for n 65 1
Instantons on ALE spaces and Super Liouville Conformal Field Theories
We provide evidence that the conformal blocks of N=1 super Liouville
conformal field theory are described in terms of the SU(2) Nekrasov partition
function on the ALE space O_{P^1}(-2).Comment: 10 page
Cohomology of skew-holomorphic Lie algebroids
We introduce the notion of skew-holomorphic Lie algebroid on a complex
manifold, and explore some cohomologies theories that one can associate to it.
Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys.
(incorporates only very minor changes
Parafermionic Liouville field theory and instantons on ALE spaces
In this paper we study the correspondence between the
coset conformal field
theories and SU(n) gauge theories on
. Namely we check the correspondence between the
SU(2) Nekrasov partition function on and the
conformal blocks of the parafermion algebra (in and modules).
We find that they are equal up to the U(1)-factor as it was in all cases of
AGT-like relations. Studying the structure of the instanton partition function
on we also find some evidence that this
correspondence with arbitrary takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version
to appear in JHE
Quantitative lung ultrasonography: A putative new algorithm for automatic detection and quantification of B-lines
Background: This pilot study was designed to develop a fully automatic and quantitative scoring system of B-lines (QLUSS: quantitative lung ultrasound score) involving the pleural line and to compare it with previously described semi-quantitative scores in the measurement of extravascular lung water as determined by standard thermo-dilution. Methods: This was a prospective observational study of 12 patients admitted in the intensive care unit with acute respiratory distress and each provided with 12 lung ultrasound (LUS) frames. Data collected from each patient consisted in five different scores, four semi-quantitative (nLUSS, cLUSS, qLUSS, %LUSS) and quantitative scores (QLUSS). The association between LUS scores and extravascular lung water (EVLW) was determined by simple linear regression (SLR) and robust linear regression (RLR) methods. A correlation analysis between the LUS scores was performed by using the Spearman rank test. Inter-observer variability was tested by computing intraclass correlation coefficient (ICC) in two-way models for agreement, basing on scores obtained by different raters blinded to patients' conditions and clinical history. Results: In the SLR, QLUSS showed a stronger association with EVLW (R 2 = 0.57) than cLUSS (R 2 = 0.45) and nLUSS (R 2 = 0.000), while a lower association than qLUSS (R 2 = 0.85) and %LUSS (R 2 = 0.72) occurred. By applying RLR, QLUSS showed an association for EVLW (R 2 = 0.86) comparable to qLUSS (R 2 = 0.85) and stronger than %LUSS (R 2 = 0.72). QLUSS was significantly correlated with qLUSS (r = 0.772; p = 0.003) and %LUSS (r = 0.757; p = 0.005), but not with cLUSS (r = 0.561; p = 0.058) and nLUSS (r = 0.105; p = 0.744). Moreover, QLUSS showed the highest ICC (0.998; 95%CI from 0.996 to 0.999) among the LUS scores. Conclusions: This study demonstrates that computer-aided scoring of the pleural line percentage affected by B-lines has the potential to assess EVLW. QLUSS may have a significant impact, once validated with a larger dataset composed by multiple real-time frames. This approach has the potentials to be advantageous in terms of faster data analysis and applicability to large sets of data without increased costs. On the contrary, it is not useful in pleural effusion or consolidations
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