158 research outputs found
-Riemann-Roch for singular complex curves
We present a comprehensive -theory for the -operator
on singular complex curves, including -versions of the Riemann-Roch
theorem and some applications.Comment: 19 page
Modifications of torsion-free coherent analytic sheaves
We study the transformation of torsion-free coherent analytic sheaves under
proper modifications. More precisely, we study direct images of inverse image
sheaves, and torsion-free preimages of direct image sheaves. Under some
conditions, it is shown that torsion-free coherent sheaves can be realized as
the direct image of locally free sheaves under modifications. Thus, it is
possible to study coherent sheaves modulo torsion by reducing the problem to
study vector bundles on manifolds. We apply this to reduced ideal sheaves and
to the Grauert-Riemenschneider canonical sheaf of holomorphic n-forms.Comment: 28 pages; the article has been completely rewritten due to a wrong
statement in the first versio
A generalization of Takegoshi's relative vanishing theorem
We present a generalization of Takegoshi's relative version of the
Grauert-Riemenschneider vanishing theorem. Under some natural assumptions, we
extend Takegoshi's vanishing theorem to the case of Nakano semi-positive
coherent analytic sheaves on singular complex spaces. We also obtain some new
results about proper modifications of torsion-free coherent analytic sheaves.Comment: 21 pages - We fixed a mistake by adding Hausdorff-condition
Chern forms of singular metrics on vector bundles
We study singular hermitian metrics on holomorphic vector bundles, following
Berndtsson-P{\u{a}}un. Previous work by Raufi has shown that for such metrics,
it is in general not possible to define the curvature as a current with measure
coefficients. In this paper we show that despite this, under appropriate
codimension restrictions on the singular set of the metric, it is still
possible to define Chern forms as closed currents of order 0 with locally
finite mass, which represent the Chern classes of the vector bundle.Comment: 18
On Lelong Numbers of Generalized Monge-Amp\`ere Products
We consider generalized (mixed) Monge-Amp\`ere products of
quasiplurisubharmonic functions (with and without analytic singularities) as
they were introduced and studied in several articles written by subsets of M.
Andersson, E. Wulcan, Z. B{\l}ocki, R. L\"ark\"ang, H. Raufi, J. Ruppenthal,
and the author. We continue these studies and present estimates for the Lelong
numbers of pushforwards of such products by proper holomorphic submersions.
Furthermore, we apply these estimates to Chern and Segre currents of
pseudoeffective vector bundles. Among other corollaries, we obtain the
following generalization of a recent result by X. Wu. If the non-nef locus of a
pseudoeffective vector bundle on a K\"ahler manifold is contained in a
countable union of -codimensional analytic sets, and if the -power of the
first Chern class of is trivial, then is nef.Comment: 32 pages; minor corrections in the second versio
Chern forms of hermitian metrics with analytic singularities on vector bundles
We define Chern and Segre forms, or rather currents, associated with a
Griffiths positive singular hermitian metric with analytic singularities on
a holomorphic vector bundle . The currents are constructed as pushforwards
of generalized Monge-Amp\`ere products on the projectivization of . The
Chern and Segre currents represent the Chern and Segre classes of ,
respectively, and coincide with the Chern and Segre forms of and , where
is smooth. Moreover, our currents coincide with the Chern and Segre forms
constructed by the first three authors and Ruppenthal in the cases when these
are defined
Feasibility of state of the art PET/CT systems performance harmonisation
Purpose The objective of this study was to explore the feasibility of harmonising performance for PET/CT systems equipped with time-of-flight (ToF) and resolution modelling/point spread function (PSF) technologies. A second aim was producing a working prototype of new harmonising criteria with higher contrast recoveries than current EARL standards using various SUV metrics. Methods Four PET/CT systems with both ToF and PSF capabilities from three major vendors were used to acquire and reconstruct images of the NEMA NU2-2007 body phantom filled conforming EANM EARL guidelines. A total of 15 reconstruction parameter sets of varying pixel size, post filtering and reconstruction type, with three different acquisition durations were used to compare the quantitative performance of the systems. A target range for recovery curves was established such that it would accommodate the highest matching recoveries from all investigated systems. These updated criteria were validated on 18 additional scanners from 16 sites in order to demonstrate the scanners' ability to meet the new target range. Results Each of the four systems was found to be capable of producing harmonising reconstructions with similar recovery curves. The five reconstruction parameter sets producing harmonising results significantly increased SUVmean (25%) and SUVmax (26%) contrast recoveries compared with current EARL specifications. Additional prospective validation performed on 18 scanners from 16 EARL accredited sites demonstrated the feasibility of updated harmonising specifications. SUVpeak was found to significantly reduce the variability in quantitative results while producing lower recoveries in smaller ( Conclusions Harmonising PET/CT systems with ToF and PSF technologies from different vendors was found to be feasible. The harmonisation of such systems would require an update to the current multicentre accreditation program EARL in order to accommodate higher recoveries. SUVpeak should be further investigated as a noise resistant alternative quantitative metric to SUVmax
The Importance of Slow-roll Corrections During Multi-field Inflation
We re-examine the importance of slow-roll corrections during the evolution of
cosmological perturbations in models of multi-field inflation. We find that in
many instances the presence of light degrees of freedom leads to situations in
which next to leading order slow-roll corrections become significant. Examples
where we expect such corrections to be crucial include models in which modes
exit the Hubble radius while the inflationary trajectory undergoes an abrupt
turn in field space, or during a phase transition. We illustrate this with two
examples -- hybrid inflation and double quadratic inflation. Utilizing both
analytic estimates and full numerical results, we find that corrections can be
as large as 20%. Our results have implications for many existing models in the
literature, as these corrections must be included to obtain accurate
observational predictions -- particularly given the level of accuracy expected
from CMB experiments such as PlanckComment: v1: 21 pages, 3 figures, 1 appendix. v2: clarifications to
{\S}{\S}2.1, 3.1 and 4, {\S}5.3 added, references added, results unchanged.
Matches published version in JCA
- …