1,720,990 research outputs found
Slope inequalities for fibred surfaces via GIT
Full text linkIn this paper we present a generalisation of a theorem due to Cornalba and Harris, which is an application of Geometric Invariant Theory to the study of invariants of fibrations. In particular, our generalisation makes it possible to treat the problem of bounding the invariants of general fibred surfaces. As a first application, we give a new proof of the slope inequality and of a bound for the invariants associated to double cover fibrations
Fibrations of Campana general type on surfaces
Full text linkWe construct complex surfaces with genus two fibrations over P^1 having special fibres such that the minimum of the multiplicities of the components is ≥ 2 whereas the g.c.d is 1. We can then produce new examples of fibred surfaces without multiple fibres which are of “general type” according to the definition of Campana. We prove that these surfaces are of general type and simply connected; and we compute in some cases their invariants. Moreover, we extend the construction obtaining general type fibrations of any even genus on simply connected surfaces. All our examples are defined over number field
Slopes of trigonal fibred surfaces and of higher dimensional fibrations
No full textWe prove a sharp lower bound for the slope of trigonal fibrations of even genus and general Maroni invariant using a method of Cornalba-Harris
Higher-dimensional Clifford-Severi equalities
Full text linkLet X be a smooth complex projective variety, a: X → A a morphism to an abelian variety such that pic0(A) injects into pic0(X) and let L be a line bundle on X; denote by ha0(X,L) the minimum of h0(X,LS - a-α) for α Pic0(A). The so-called Clifford-Severi inequalities have been proven in [M. A. Barja, Generalized Clifford-Severi inequality and the volume of irregular varieties, Duke Math. J. 164(3) (2015) 541-568; M. A. Barja, R. Pardini and L. Stoppino, Linear systems on irregular varieties, J. Inst. Math. Jussieu (2019) 1-39; doi:10.1017/S1474748019000069]; in particular, for any L there is a lower bound for the volume given by: vol(L) ≥ n!ha0(X,L), and, if KX - L is pseudoeffective, vol(L) ≥ 2n!ha0(X,L). In this paper, we characterize varieties and line bundles for which the above Clifford-Severi inequalities are equalities
Stability and singularities of relative hypersurfaces
Full text linkWe study relative hypersurfaces over curves, and prove an instability
condition for the fibres. This gives an upper bound on the log canonical
threshold of the relative hypersurface. We compare these results with the
information that can be derived from Nakayama's Zariski decomposition of
effective divisors on relative projective bundles.Comment: 26 pages, 1 figure, revised version with minor change
LINEAR SYSTEMS on IRREGULAR VARIETIES
Full text linkLet be a normal complex projective variety, a subvariety of dimension (possibly) and a morphism to an abelian variety such that injects into; let be a line bundle on and a general element.We introduce two new ingredients for the study of linear systems on. First of all, we show the existence of a factorization of the map, called the eventual map of on, which controls the behavior of the linear systems, asymptotically with respect to the pullbacks to the connected étale covers induced by the -th multiplication map of.Second, we define the so-called continuous rank function, where is the pullback of an ample divisor of. This function extends to a continuous function of, which is differentiable except possibly at countably many points; when we compute the left derivative explicitly.As an application, we give quick short proofs of a wide range of new Clifford-Severi inequalities, i.e., geographical bounds of the form where depends on several geometrical properties of, or
MRI study of small bowel in Crohn’s disease: evaluation of disease activity with oral preparation and e.v. gadolinium diethylenetriamine pentaacetic acid.
No full text
Diffusion-Weighted MRI with parallel imaging technique: apparent diffusion coefficient determination in normal kidneys and in nonmalignant renal disease
No full textThe purpose of the study was to assess the capability and the reliability of apparent diffusion coefficient (ADC) measurements in the
evaluation of different benign renal abnormalities. Twenty-five healthy volunteers and 31 patients, divided into seven different groups (A–G)
according to pathology, underwent diffusion-weighted magnetic resonance imaging (DW MRI) of the kidneys using 1.5-T system. DW
images were obtained in the axial plane with a spin-echo echo planar imaging single-shot sequence with three b values (0, 300, and
600 s/mm2). Before acquisition of DW sequences, we performed in each patient a morphological study of the kidneys. ADC was
2.40±0.20×10−3 mm2 s−1 in volunteers. A significant difference was found between Groups A (cysts=3.39±0.51×10−3 mm2 s−1) and B
(acute/chronic renal failure=1.38±0.40×10−3 mm2 s−1) and between Groups A and C (chronic pyelonephritis=1.53±0.21×10−3 mm2 s−1)
(Pb.05). An important difference was also observed among Group D (hydronephrosis=4.82±0.35×10−3 mm2 s−1) and Groups A, B, and C
(Pb.05), whereas no differences were found between Groups B and C (PN.05). A considerable correlation between glomerular filtration rate
and ADC was found (P=.04). In conclusion, significant differences were detected among different patient groups, and this suggests that ADC
measurements can be useful in differentiating normal renal parenchyma from most commonly encountered nonmalignant renal lesion
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