Nodal curves with general moduli on K3 surfaces

We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a d-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p-2, for p any integer between 3 and 11 and g = p - d between 2 and p. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S,X) to the moduli space of curves of genus g that associates to X the isomorphism class [C] of its normalization.Comment: 12 pages. Submitted preprin

Ulrich bundles on a general blow–up of the plane

We prove that on Xn, the plane blown–up at n general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree m passing simply through the n blown–up points, with m less than or equal to 2 times the square root of n 2, and such that the line bundle in question is very ample on Xn. We prove that the number of these Ulrich line bundles tends to infinity with n. We also prove the existence of slope–stable rank–r Ulrich vector bundles on Xn, for n > 2 and any r > 1 and we compute the dimensions of their moduli spaces. These computations imply that Xn is Ulrich wil

The subchondral bone in articular cartilage repair: current problems in the surgical management

As the understanding of interactions between articular cartilage and subchondral bone continues to evolve, increased attention is being directed at treatment options for the entire osteochondral unit, rather than focusing on the articular surface only. It is becoming apparent that without support from an intact subchondral bed, any treatment of the surface chondral lesion is likely to fail. This article reviews issues affecting the entire osteochondral unit, such as subchondral changes after marrow-stimulation techniques and meniscectomy or large osteochondral defects created by prosthetic resurfacing techniques. Also discussed are surgical techniques designed to address these issues, including the use of osteochondral allografts, autologous bone grafting, next generation cell-based implants, as well as strategies after failed subchondral repair and problems specific to the ankle joint. Lastly, since this area remains in constant evolution, the requirements for prospective studies needed to evaluate these emerging technologies will be reviewed

Severi varieties and Brill\u2013Noether theory of curves on abelian surfaces

Severi varieties and Brill\u2013Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface S with polarization L of type (1,n), we prove nonemptiness and regularity of the Severi variety parametrizing \u3b4-nodal curves in the linear system |L| for 0 64\u3b4 64n 121=p 122 (here p is the arithmetic genus of any curve in |L|). We also show that a general genus g curve having as nodal model a hyperplane section of some (1,n)-polarized abelian surface admits only finitely many such models up to translation; moreover, any such model lies on finitely many (1,n)-polarized abelian surfaces. Under certain assumptions, a conjecture of Dedieu and Sernesi is proved concerning the possibility of deforming a genus g curve in S equigenerically to a nodal curve. The rest of the paper deals with the Brill\u2013Noether theory of curves in |L|. It turns out that a general curve in |L| is Brill\u2013Noether general. However, as soon as the Brill\u2013Noether number is negative and some other inequalities are satisfied, the locus |L|rd of smooth curves in |L| possessing a grd is nonempty and has a component of the expected dimension. As an application, we obtain the existence of a component of the Brill\u2013Noether locus Mrp,d having the expected codimension in the moduli space of curves Mp. For r=1, the results are generalized to nodal curves

Autologous chondrocyte implantation versus ACI using 3D-bioresorbable graft for the treatment of large full-thickness cartilage lesions of the knee

BACKGROUND: In autologous chondrocyte implantation (ACI), the periosteum patch which is sutured over the cartilage defect has been identified as a major source of complications such as periosteal hypertrophy. In the present retrospective study, we compared midterm results of first-generation ACI with a periosteal patch to second generation ACI using a biodegradable collagen fleece (BioSeed-C) in 82 patients suffering from chronic posttraumatic and degenerative cartilage lesions of the knee. METHODS: Clinical outcome was assessed in 42 patients of group 1 and in 40 patients of group 2 before implantation of the autologous chondrocytes and at a minimum follow-up of 2 years using the ICRS score, the modified Cincinnati score and the Lysholm score. RESULTS: Although patients treated with BioSeed-C had more previous surgical procedures on their respective knees, highly significant improvements (P < 0.001) were assessed in both groups at comparable outcome levels: the ICRS score improved from grade D (poor) preoperatively to grade C (fair); the modified Cincinnati knee score from 3.26 to 6.4 (group 1) and 3.3 and 6.88 (group 2). Lysholm score improved from 33 to 70 points (group 1) and from 47 to 78 points (group 2), respectively. Revision surgery was due to symptomatic periosteal hypertrophy (n = 4), graft failure (n = 3), plica syndrome (n = 2) synovectomy (n = 1) (group 1); and graft failure (n = 2), debridement (n = 1), synovectomy (n = 2) (group 2). CONCLUSION: These results suggest that BioSeed-C is an equally effective treatment option for focal degenerative chondral lesions of the knee in this challenging and complex patient profile