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We study varieties X \subset \mathbb {P}^r such that N_X^*(k) is an Ulrich vector bundle for some integer k. We first prove that such an X must be a curve. Then we give several examples of curves with N_X^*(k) an Ulrich vector bundle. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a particular class of rank two vector bundles (instanton bundles) on the Fano threefold of index one F : = F 1 × P 1. We show that every instanton bundle on F can be described as the cohomology of a monad whose terms are free sheaves. Furthermore we prove the existence of instanton bundles for any admissible second Chern class and we construct a nice component of the moduli space where they sit. Finally we show that minimal instanton bundles (i.e., with the least possible degree of the second Chern class) are aCM and we describe their moduli space. [ABSTRACT FROM AUTHOR]

In this work we characterize Ulrich bundles of any rank on polarized rational ruled surfaces over P 1 . We show that every Ulrich bundle admits a resolution in terms of line bundles. Conversely, given an injective map between suitable totally decomposed vector bundles, we show that its cokernel is Ulrich if it satisfies a vanishing in cohomology. As a consequence we obtain, once we fix a polarization, the existence of Ulrich bundles for any admissible rank and first Chern class. Moreover we show the existence of stable Ulrich bundles for certain pairs (rk (E) , c 1 (E)) and with respect to a family of polarizations. Finally we construct examples of indecomposable Ulrich bundles for several different polarizations and ranks. [ABSTRACT FROM AUTHOR]

Cranioplasty is the surgical technology employed to repair a traumatic head injury, cerebrovascular disease, oncology resection and congenital anomalies. Actually, different bone substitutes are used, either derived from biological products such as hydroxyapatite and demineralized bone matrix or synthetic ones such as sulfate or phosphate ceramics and polymer-based substitutes. Considering that the choice of the best material for cranioplasty is controversial, linked to the best operation procedure, the intent of this review was to report the outcome of research conducted on materials used for such applications, comparing the most used materials. The most interesting challenge is to preserve the mechanical properties while improving the bioactivity, porosity, biocompatibility, antibacterial properties, lowering thickness and costs. Among polymer materials, polymethylmethacrylate and polyetheretherketone are the most motivating, due to their biocompatibility, rigidity and toughness. Other biomaterials, with ecofriendly attributes, such as polycaprolactone and polylactic acid have been investigated, due to their microstructure that mimic the trabecular bone, encouraging vascularization and cell–cell communications. Taking into consideration that each material must be selected for specific clinical use, the main limitation remains the defects and the lack of vascularization, consequently porous synthetic substitutes could be an interesting way to support a faster and wider vascularization, with the aim to improve patient prognosis. [ABSTRACT FROM AUTHOR]