Search

We prove that the linear syzygy spaces of a general canonical curve are spanned by syzygies of minimal rank. [ABSTRACT FROM AUTHOR]

We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri's theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math 190:603-646, 2012) and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Secondly, in the case of curves of even genus, we enhance Voisin's Theorem by providing a structure theorem for the last syzygy space, resolving the Geometric Syzygy Conjecture in even genus. [ABSTRACT FROM AUTHOR]

We construct Eagon–Northcott cycles on Hurwitz space and compare their classes to Kleiman's multiple point loci. Applying this construction towards the classification of Betti tables of canonical curves, we find that the value of the extremal Betti number records the number of minimal pencils. The result holds under transversality hypotheses equivalent to the virtual cycles having a geometric interpretation. We analyze the case of two minimal pencils, showing that the transversality hypotheses hold generically. [ABSTRACT FROM AUTHOR]

Using lattice theory on special $$K3$$ surfaces, calculations on moduli stacks of pointed curves and Voisin's proof of Green's Conjecture on syzygies of canonical curves, we prove the Prym-Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus, as well as (many cases of) the Green-Lazarsfeld Secant Conjecture on syzygies of non-special line bundles on general curves. [ABSTRACT FROM AUTHOR]

In this article we consider moduli properties of singular curves on K3 surfaces. Let B g denote the stack of primitively polarized K3 surfaces ( X , L ) of genus g and let T g , k n → B g be the stack parameterizing tuples [ ( f : C → X , L ) ] with f an unramified morphism which is birational onto its image, C a smooth curve of genus p ( g , k ) − n and f ⁎ C ∈ | k L | . We show that the forgetful morphism η : T g , k n → M p ( g , k ) − n is generically finite on at least one component, for all but finitely many values of p ( g , k ) − n . We further study the Brill–Noether theory of those curves parametrized by the image of η , and find a Wahl-type obstruction for a smooth curve with an unordered marking to have a nodal model on a K3 surface in such a way that the marking is the divisor over the nodes. [ABSTRACT FROM AUTHOR]

We investigate the universal Severi variety of rational curves on K3 surfaces, which parametrizes irreducible rational curves in a fixed class on varying K3 surfaces of fixed genus. We investigate the conjectured irreducibility of this space in the case of primitive classes using the deformation theory of stable maps and obtain partial results. Furthermore, we give a short proof of the irreducibility of universal Severi varieties of high-genus curves on K3 surfaces. [ABSTRACT FROM PUBLISHER]

We prove two statements concerning the linear strand of the minimal free resolution of a k -gonal curve C of genus g. Firstly, we show that a general curve C of genus g of non-maximal gonality k ≤ g + 1 2 satisfies Schreyer's Conjecture, that is, b g − k , 1 (C , ω C) = g − k. This statement goes beyond Green's Conjecture and predicts that all highest order linear syzygies in the canonical embedding of C are determined by the syzygies of the (k − 1) -dimensional scroll containing C. Secondly, we prove an optimal effective version of the Gonality Conjecture for general k -gonal curves, which makes more precise the (asymptotic) Gonality Conjecture proved by Ein–Lazarsfeld and improves results of Rathmann. [ABSTRACT FROM AUTHOR]

The roles of NK cells, surfactant protein D (SP-D), and IFNγ, as well as the effect of ozone (O3) inhalation, were studied on recirculation of pulmonary dendritic cells (DC) to the mediastinal lymph nodes.O3 exposure and lack of SP-D reduced NK cell IFNγ and lung tissue CCL21 mRNA expression and impaired DC homing to the mediastinal lymph nodes. Notably, addition of recombinant SP-D to naive mononuclear cells stimulated IFNγ release in vitro. Because NKp46, a glycosylated membrane receptor, was necessary for dosedependent SP-D binding to NK cells in vitro and DC migration in vivo, we speculate that SP-D may constitutively stimulate IFNγ production by NK cells, possibly via NKp46. This mechanism could then initiate the IFN-7/IL-I2 feedback circuit, a key amplifier of DC lymph node homing. Inhibition of this process during an acute inflammatory response causes DC retention in the peripheral lung tissue and contributes to injury. [ABSTRACT FROM AUTHOR]

Systemic Lupus Erythematosus (SLE) is a chronic autoimmune disorder characterized by broad clinical manifestations including cardiovascular and renal complications with periodic disease flares and significant morbidity and mortality. One of the main contributing factors to the pathology of SLE is the accumulation and impaired clearance of immune complexes of which the principle components are host auto-antigens and antibodies. The contribution of host lipids to the formation of these autoimmune complexes remains poorly defined. The aim of the present study was to identify and analyze candidate lipid autoantigens and their corresponding anti–lipid antibody responses in a well-defined SLE patient cohort using a combination of immunological and biophysical techniques. Disease monitoring in the SLE cohort was undertaken with serial British Isles Lupus Assessment Group (BILAG) scoring. Correlations between specific lipid/anti-lipid responses were investigated as disease activity developed from active flares to quiescent during a follow up period. We report a significant negative correlation between anti-lipid antibodies for 24S-hydroxycholesterol, cardiolipin and phosphatidylserine with SLE disease activity. Taken together, these data suggest that lipid autoantigens represent a new family of biomarkers that can be employed to monitor disease activity plus the efficacy of therapeutic intervention in SLE. [ABSTRACT FROM AUTHOR]